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We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic self-dual codes over $GR(4, 2)$ are constructed. Euclidean self-dual codes give self-dual $\mathbb Z_4$−codes. Hermitian self-dual codes yield 3−modular lattices and quasi-cyclic self-dual $\mathbb Z_4$−codes.