a study on structure of codes over mathbb z_4+umathbb z_4+vmathbb z_4

We study $(1+2u+2v)$-constacyclic code over a semi-local ring $s=mathbb z_4+umathbb z_4+vmathbb z_4$ with the condition $u^2=3u,v^2=3v$, and $uv=vu=0$,  we show that  $(1+2u+2v)$-constacyclic code over $s$ is equivalent to quasi-cyclic code over $mathbb{z}_4$ by using two new gray maps from $s$ to $mathbb{z}_4.$ also, for odd length $n$ we have defined a generating set for constacyclic codes over $s.$ finally, we obtained some examples which are new to the data base [database of $mathbb{z}_4$ codes [online]}, http://$mathbb{z}_4$ codes.info(accessed march 2, 2020)].