  Let $p$ be a prime number. In this paper, we study cyclic codes over the ring
$ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$. We find a unique set of
generators for these codes. We also study the rank and the Hamming distance of
these codes. We obtain all except one ternary optimal code of length 12 as the
Gray image of the cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2,
uv-vu\rangle$. We also characterize the $p$-ary image of these cyclic codes
under the Gray map.
