  We present a list decoding algorithm for quaternary negacyclic codes over the
Lee metric. To achieve this result, we use a Sudan-Guruswami type list decoding
algorithm for Reed-Solomon codes over certain ring alphabets. Our decoding
strategy for negacyclic codes over the ring $\mathbb Z_4$ combines the list
decoding algorithm by Wu with the Gr\"obner basis approach for solving a key
equation due to Byrne and Fitzpatrick.
