In this paper, we explore skew cyclic codes over the ring \(R = \mathbb{Z}_4 + u\mathbb{Z}_4 + v\mathbb{Z}_4\) , where \(u^2 = u\) , \(v^2 = v\) , and \(uv = vu = 0\) . We consider an automorphism θ and explore generating sets of skew cyclic codes over R. We give a decomposition of linear codes over R and then use it to characterise skew cyclic codes. We define a Gray map to get codes over \(\mathbb{Z}_4\) and provide several examples of new codes obtained using it.
