  The sizes of optimal constant-composition codes of weight three have been
determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes
played an important role in their constructions. In this paper, we study the
problem of constructing optimal quaternary constant-composition codes with
Hamming weight four and minimum distances five or six through group divisible
codes and Room square approaches. The problem is solved leaving only five
lengths undetermined. Previously, the results on the sizes of such quaternary
constant-composition codes were scarce.
