  We convert Stern's information set decoding (ISD) algorithm to the ring
$\mathbb{Z}/4 \mathbb{Z}$ equipped with the Lee metric. Moreover, we set up the
general framework for a McEliece and a Niederreiter cryptosystem over this
ring. The complexity of the ISD algorithm determines the minimum key size in
these cryptosystems for a given security level. We show that using Lee metric
codes can drastically decrease the key size, compared to Hamming metric codes.
In the end we explain how our results can be generalized to other Galois rings
$\mathbb{Z}/p^s\mathbb{Z}$.
