  Z2Z4-additive codes have been defined as a subgroup of Z2^{r} x Z4^{s} in [5]
where Z2, Z4 are the rings of integers modulo 2 and 4 respectively and r and s
positive integers. In this study, we define a new family of codes over the set
Z2^{r}[\bar{\xi}] x Z4^{s}[\xi] where \xi is the root of a monic basic
primitive polynomial in Z4[x]. We give the standard form of the generator and
parity-check matrices of codes over Z2^{r}[\bar{\xi}] x Z4^{s}[\xi] and also we
introduce skew cyclic codes and their spanning sets over this set.
