In this paper, we investigate the algebraic structure of the non-chain ring followed by the description of its group automorphisms to get the algebraic structure of codes and their dual over this ring. Further, we explore the algebraic structure of  skew-constacyclic codes by showing that their images by a linear Gray map are skew-multi-twisted codes and determine their generator polynomials. Finally, we characterize self-dual skew-constacyclic codes over and give conditions on the existence of self-dual skew cyclic and self-dual skew negacyclic codes over

non-chain ring, skew-constacyclic codes, Gray map, self-dual skew codes, skew-multi-twisted codes.