Chevy Truck Electrical Problem

I have a 99 Silverado 5.3L
I'm having problems with the battery discharging until dead. I have replaced the battery and alternator twice in the last 2 months. I have re-charged the battery and the vehicle will start, but instantly the powerdrain begins and within 5 min the truck dies. The alternator is putting out 14 volts. I placed a scanner on it and it shows a diagnostic code of
( alternator L terminal ckt ) My tester is able to test whatever this code is but my truck evidently is not able too or is not programmed to provide such a test. I've spent alot of time looking over all the wiring for shorts or grounds and everything look good and tight. I can put my multimeter on the battery with the vehicle shut off and you can see the voltage slowly drop. Any suggestions would be greatly appreciated.

Kind Regards~