  In this note, we study the classification of $\mathbb{Z}_4$-codes. For some
special cases $(k_1,k_2)$, by hand, we give a classification of
$\mathbb{Z}_4$-codes of length $n$ and type $4^{k_1}2^{k_2}$ satisfying a
certain condition. Our exhaustive computer search completes the classification
of $\mathbb{Z}_4$-codes of lengths up to $7$.
