  In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic
codes and their skew codes over the finite ring R=Z_3+vZ_3+v^2Z_3, v^3=v. The
Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic and skew
constacyclic codes over R are obtained. A necessary and sufficient condition
for cyclic (negacyclic) codes over R that contains its dual has been given. The
parameters of quantum error correcting codes are obtained from both cyclic and
negacyclic codes over R. It is given some examples. Firstly, quasi-constacyclic
and skew quasi-constacyclic codes are introduced. By giving two product, it is
investigated their duality. A sufficient condition for 1-generator skew
quasi-constacyclic codes to be free is determined.
