I think that technically isn't allowed, since the C standard requires single-byte representations of 26 uppercase + 26 lowercase + 10 numeric + 29 symbol + 1 space = 92 characters (and assorted (most of them useless) control characters), which don't fit in 64 values of a 6-bit byte.
It would interesting to see a CDC 6400 implementation of "like C, but we ignore the bit about character set and also the part where the compiler is a evil genie trying to screw you over", though.
60 bit words, 18 and 60 bit registers, 6 bit characters.