Let \(R=\mathbb {Z}_{4}+u\mathbb {Z}_{4}\) be a finite non-chain ring, where u² = 1. In this paper, we consider (σ, δ)-skew quasi-cyclic codes over the ring R, where σ is an automorphism of R and δ is an inner σ-derivation of R. We determine the structure of 1-generator (σ, δ)-skew quasi-cyclic codes over R and give a sufficient condition for 1-generator (σ, δ)-skew quasi-cyclic codes over R to be free. We also determine a distance bound for free 1-generator (σ, δ)-skew quasi-cyclic codes. Moreover, using the residue codes of these codes over R we obtain some good \(\mathbb {Z}_{4}\)-linear codes. Finally, we give the characterization of Euclidean dual codes of (σ, δ)-skew quasi-cyclic codes.

令\（R = \ mathbb {Z} _ {4} + u \ mathbb {Z} _ {4} \）是有限的非链环，其中u ² =1。在本文中，我们考虑（σ，δ）在环-skew准循环码- [R ，其中σ是的构- [R和δ是一内σ的-derivation ř。我们确定1-发生器（结构σ，δ）-skew准循环码过- [R ，并给出1-发生器（一个充分条件σ，δ）超过-skew准循环码ř自由。我们还确定了自由1生成器（σ，δ）斜准循环码的距离范围。此外，使用这些代码在R上的残差代码，可以获得一些良好的\（\ mathbb {Z} _ {4} \）线性代码。最后，给出了（σ，δ）-偏准循环码的欧几里德对偶码的刻画。