I was riding the bike for a few hours the other day, and as I was going uphill, the engine started to sputter and the check engine light came on and then shut off then after that, I noticed if I was in fifth gear and at a low RPM it would do the same thing. I have a 2004 Road King custom

 

I would check the spark plug wire to the front cylinder and see if it has shorted out on the bottom of the fuel tank. I have seen several plugs wire do exactly that.
P Codes
P0107 Map Sensor Open/Low
P0108 Map Sensor High
P0117 ET Sensor Low
P0118 ET Sensor High
P0112I AT Voltage Low
P0113I AT Voltage Open/High
P0120 TPS1 Range Error
P0220 TPS2 Range Error
P0122 TPS1 Low
P0123 TPS2 High/Open
P0131 Front Oxygen Sensor Low
P0132 Front Oxygen Sensor High
P0151 Rear Oxygen Sensor Low
P0152 Rear Oxygen Sensor High
P0154 Rear Oxygen Sensor Inactive.
P0222 TPS2 Low
P0223 TPS2 High/Open
P0261 Front Injector Open/Low
P0263 Rear Injector Open/Low
P0262 Front Injector High
P0264 Rear Injector High
P0373 CKP Sensor Intermittent
P0374 CKP Sensor Synch Error
P0444 Purge Solenoid Open/Low
P0445 Purge Solenoid High
P0562 Battery Voltage Low
P0563 Battery Voltage High
P0501 VSS Sensor Low
P0502 VSS Sensor High/Open
P0572 Brake Switch Low
P0577 Cruise Control Input High
P0603 ECM EEPROM Memory Error
P0605 ECM FLASH Memory Error
P06415 V+Vref 1 Out Of Range
P06515 V+Vref 2 Out Of Range
P1001 System Relay Coil Open/Low
P1002 System Relay Coil High/Shorted
P1003 System relay contacts open
P1004 System Relay Contacts Closed
P1009 Incorrect Password
P1010 Missing Password
P1270 TGS Validation Error
P1351 Front Driver Open/Low
P1352 Front Ignition Coil Driver High/Shorted
P1353 Front Cylinder No Combustion
P1354 Rear Ignition Coil Driver Open/Low
P1355 Rear Ignition Coil Driver High/Shorted
P1356 Rear Cylinder No Combustion
P1357 Front Cylinder Combustion Intermittent
P1358 Rear Cylinder Combustion Intermittent
P1475 Exhaust Actuation Position Error
P1477 Exhaust Actuator Open/Low
P1478 Exhaust Actuator Shorted/High
P1501 Jiffy Stand Sensor Low
P1502 Jiffy Stand Sensor High P1510 EFI Limited
Performance Mode
P1511 EFI Power Management Mode
P1512 EFI Forced Idle Mode
P1514 Air Flow Fault
P1600 EFI Module Processor Internal Error
P2100 EFI Motor Circuit Open
P2101 EFI Motor Circuit Range Performance (Actuation
Error)
P2102 EFI Motor Circuit Low
P2103 EFI Motor Circuit High
P2105 EFI Forced engine shutdown
P2107 EFI Module Processor Internal Fault
P2119 EFI Motor Throttle Body Range Performance
P2122 TGS1 Low/Open
P2123 TGS1 High
P2127 TGS2 Low/Open
P2128 TGS2 High
P2135 TPS Correlation Error
P2138 TGS Correlation Error (Twist grip sensor)
P2176 EFI Closed Position Not Learned
U Codes
U1016 Loss of ECM Serial Data
U1064 Loss of TSM/FSFM Serial Data to ECM
U1097 Loss of Speedometer Serial Data to ECM
U1255 Serial Data Error
U1300 Serial Data Low
U1301 Serial Data High
Harley Davidson 2008 DTC Code Reading (draft)
Harley Davidson DTC Codes – Unofficial Guide Page 3
B Codes
B0563 Battery Voltage High.
B1121(TSM) Left Turn Output Fault
B1121(HFSM) Left Turn Output Open
B1122(TSM) Right Turn Output Fault
B1122(HFSM) Right Turn Output Open
B1123(HFSM) Left Turn Output Short to Ground
B1124(HFSM) Right Turn Output Short to Ground
B1125(HFSM) Left Turn Output Short to Battery
B1126(HFSM) Right Turn Output Short to Battery
B1131(HFSM) Alarm Output Low
B1132(HFSM) Alarm Output High
B1134 Starter Output High
B1135 Accelerometer Failed
B1136(HFSM) Accelerometer Tip Test Error
B1141(TSM) Ignition Switch Low/Open
B1141(HFSM) Ignition Switch Low/Open
B1142 Smart Security System Internal Fault
B1143(HFSM) Security Antenna Short to Ground
B1144(HFSM) Security Antenna Short to Battery
B1145(HFSM) Security Antenna Open
B1151 Bank Angle Sensor(BAS) Short to Ground
B1152 Bank Angle Sensor(BAS) Short to Battery
B1153 Bank Angle Sensor(BAS) High
B1154 Clutch Switch Input Short to Ground
B1155 Neutral Switch Input Short to Battery

 

Since I don't know you or your riding experience...... I feel I should offer this advice...

Low rpm and high load conditions, like 5th gear low rpm and/or going uphill in a high gear & low rpm, could cause a condition called "lugging the engine". This is where the engine is straining to give you the performance (speed) you are asking for by just twisting the throttle.

That is not good for the engine, or drivetrain for many reasons.

If you are lugging the engine to the point of it sputtering badly, it can cause numerous temporary conditions that could throw temporary codes.

It is possible, by your description, that you were badly lugging the engine and it lead to temp codes being thrown. That could be why the engine light came on, then went off when you raised the rpms.

IMHO clear the codes, and take the bike on a ride. Make sure to run the engine properly.

By properly I mean, anytime you calling for more than the engine seems like it can easily give you, down shift until you are at an rpm where the engine is effortlessly accelerating or maintaining your cruise speed. Never try to push an engine that remotely sounds like it is beginning to labor... Let it breathe by downshifting to a good rpm.

If the codes come back without you lugging (straining) the engine, then it's time to diagnose the reason for the codes.

I don't mean this to be condescending, it's just your description of the issue could have been from badly lugging the engine...

If you know all this and weren't lugging the engine, then disregard...