Self-dual codes over $Z_2timesZ_4$ are subgroups of $Z_2^alpha timesZ_4^beta$ that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible
values $alpha,beta$ such that there exist a code $Csubseteq Z_2^alpha timesZ_4^beta$ are established. Moreover, the construction of a $add$-linear code for each type and possible pair $(alpha,beta)$ is given. Finally, the standard techniques of invariant theory are applied to describe the weight enumerators for each type.
Let C be an additive subgroup of $Z_{2k}^n$ for any $kgeq 1$. We define a Gray map $Phi:Z_{2k}^n longrightarrow Z_2^{kn}$ such that $Phi(codi)$ is a binary propelinear code and, hence, a Hamming-compatible group code. Moreover, $Phi$ is the unique Gr
ay map such that $Phi(C)$ is Hamming-compatible group code. Using this Gray map we discuss about the nonexistence of 1-perfect binary mixed group code.
