This is the only other case I have been able to find anywhere regarding the "CODEC ERROR" on start-up. I am experiencing the same issue with my Model 16. I spoke to Tascam twice, who said they had no information on the code. They eventually gave me information for three repair shops they contract with. I spoke to 2 out of 3; the first had never heard of it, and the second had, but said they couldn't fix it and just sent it to Tascam (presumably) for replacement.
Tascam did give me one helpful tip - that I could hold rewind and play while powering on the unit to start the firmware update. Now, because I had just purchased the unit used, it didn't have a formatted SD card. Tascam said I was out of luck because you need to unit to format the card - I figured out that the firmware files just need to be located in a folder named "UTILITY", so I just did that on my computer and it worked. I'm not sure if the firmware update helped, because the problem persisted.
I asked if there were any other shortcuts that could force the unit past the error message, but they said that was the only one. I wasn't ready to give up so I decided to see if it would work as just an interface, but with the error message, the daw wouldn't recognize the unit. Out of frustration, I just started trying random combinations of buttons to see if anything would happen - and it did.
I held down the fast-forward and record buttons while powering on the unit, and it entered what I assume is mix-down mode. While in that mode, the daw was able to recognize the unit with no issues. I don't know why, but after all of that, that same power-up procedure successfully powers up the unit with no issues at all, entering the standard mode on the unit. The problem is still intermittent, but holding down fast-forward and record while flipping the power button works every time.
tl/dr: Hold down the fast-forward and record buttons while powering up to start unit successfully without the "CODEC" error message