I had this problem with my Z06. Same codes and all. I checked the connections to my battery, and everything was fine. I then went to my local "Auto Parts Store" to get my Alternator checked. They tested it and told me my Alternator was bad. Before buying a new Alternator i decided to go home and recheck everything connected to the battery. That led me to the Starter. So i disconnected the battery and i jacked my car up and looked at the connections. I took off the nut that secured the "3" Ring Terminals. Before i took the Ring Terminals off the bolt, i tugged at them. The Red wire was fine, but when i tugged at the Grey wire it just broke loose. I didn't even use that much force, it just came off like that. I checked out the wire strands and where the wires and Ring Terminal met, they were both corroded pretty bad. I decided to just get a new Ring Terminal for it instead of trying to clean the old one up. I bought some 5/16" Ring Terminals and some Dielectric Grease(Small package at the front register). I got home and went to work. I first cut off all the corroded wire strands and then cut off about 1/4" of insulation to expose the fresh copper wire strands. I then twisted the strands to get a nice spiral out of the wire so i wouldn't have any strands sticking out. I put the wire through the Ring Terminal insulation just far enough so it wouldn't stick out past the insulation, i then crimped it and tugged at it, just in case. I cleaned the other Ring Terminals and lubricated all 3 of them and the Starter Bolt with the Dielectric Grease. I then put everything back the way they were when i first started. I put my car back on the ground and reconnected the battery. I tried to start my car up and to my surprise, it did, but this time with no "Charge System Fault" or any codes(been like that for the past 3 months). My Voltage went straight to 14 volts. Well, after about 20 seconds or so. I hope this ends up being your problem. I'd rather spend $5 for the Ring Terminals and Grease, then for a new $200-300 Alternator. I'd rather use that money for future mods

. I tried to put it as simple as i could and hope everything works out for you. If you have any questions just PM me.
Danny