Let $R$ = $mathbb{F}_{p}+umathbb{F}_{p}+vmathbb{F}_{p}+uvmathbb{F}_{p}$, where u2=u, v2 and uv=vu. A relation between the support weight distribution of a linear code $mathscr{C}$ of type p4k over R and its dual code $mathscr{C}^{ot}$ is established.

The definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator over Mn×s(F2[u,v]/) are introduced, and the MacWilliams identities with respect to the RT metric for these two weight enumerators of linear codes over Mn×s(F2[u,v]/) are obtained. Finally, we give two examples to illustrate the results we obtained.