  In this paper, two different Gray-like maps from $Z_p^\alpha\times
Z_{p^k}^\beta$, where $p$ is prime, to $Z_p^n$, $n={\alpha+\beta p^{k-1}}$,
denoted by $\phi$ and $\Phi$, respectively, are presented. We have determined
the connection between the weight enumerators among the image codes under these
two mappings. We show that if $C$ is a $Z_p Z_{p^k}$-additive code, and
$C^\bot$ is its dual, then the weight enumerators of the image $p$-ary codes
$\phi(C)$ and $\Phi(C^\bot)$ are formally dual. This is a partial
generalization of [On $Z_{2^k}$-dual binary codes, arXiv:math/0509325], and the
result is generalized to odd characteristic $p$ and mixed alphabet.
Additionally, a construction of $1$-perfect additive codes in the mixed $Z_p
Z_{p^2} ... Z_{p^k}$ alphabet is given.
