  A structure theorem of the group codes which are relative projective for the
subgroup $\lbrace 1 \rbrace$ of $G$ is given. With this, we show that all such
relative projective group codes in a fixed group algebra $RG$ are in bijection
to the chains of projective group codes of length $\ell$ in the group algebra
$\mathbb{F}G$, where $\mathbb{F}$ is the residue field of $R$. We use a given
chain to construct the dual code in $RG$ and also derive the minimum Hamming
weight as well as a lower bound of the minimum euclidean weight.
