Since the column driver needs only twelve states which recycle after the 12 state, I might use 12 flip-flops wired as a ring counter The 12 flip-flops are easy to decode, but you need lots of extra logic to steer the flops into the correct starting value (set one, clear the other 11).
You could also a four bit binary counter wired to count 0 to 11 (12 states out of a possible 16). The binary counter could be decoded with a 4 line to sixteen output decoder or 2ea 3 line to eight output decoders.
You could also use six flip-flops wired as a Johnson counter (12 states out of a possible 64). To decode this, you would use 12 XOR gates.