It seems all Jap cars have questionable mileage, however 77 sounds more realistic than 38.
11K is pretty cheap especially if it's a later model? What year is it? I've seem 1990 models fetching upto 15K.
My mate just bought a black 1991 GTS-t, fairly clean for $13,800 with 97K and is wrapped.
If it looks good, drives well, what have you really got to lose. Go for it I'd say!