There has been a recent growth of interest in codes with respect to a newly defined non-Hamming metric grown as the Rosenbloom-Tsfasman metric (RT, or $ ho$, in short). In this paper, the definitions of the Lee complete $ ho$ weight enumerator and the exact complete $ ho$ weight enumerator of a code over $M_n_ imes_s(Z_4)$ are given, and the MacWilliams identities with respect to this RT metric for the two weight enumerators of a linear code over $M_n_ imes_s(Z_4)$ are proven too. At last, we also prove that the MacWilliams identities for the Lee and exact complete $ ho$ weight enumerators of a linear code over $M_n_ imes_s(Z_4)$ are the generalizations of the MacWilliams identities for the Lee and complete weight enumerators of the corresponding code over $Z_4$.