  Let $R$ be a finite commutative chain ring, $D_{2n}$ be the dihedral group of
size $2n$ and $R[D_{2n}]$ be the dihedral group ring. In this paper, we
completely characterize left ideals of $R[D_{2n}]$ (called left $D_{2n}$-codes)
when ${\rm gcd}(char(R),n)=1$. In this way, we explore the structure of some
skew-cyclic codes of length 2 over $R$ and also over $R\times S$, where $S$ is
an isomorphic copy of $R$. As a particular result, we give the structure of
cyclic codes of length 2 over $R$. In the case where $R=\F_{p^m}$ is a Galois
field, we give a classification for left $D_{2N}$-codes over $\F_{p^m}$, for
any positive integer $N$. In both cases we determine dual codes and identify
self-dual ones.
