  In this paper, we give decompositions of the moonshine module $V^{\natural}$
with respect to subVOAs associated to extremal Type II codes over $Z_{2k}$ for
an integer $k\ge2$. Those subVOAs are isomorphic to the tensor product of 24
copies of the charge conjugation orbifold VOA. Using such decompositions, we
obtain some elements of type 4A (k odd) and 2B (k even) of the Monster simple
group Aut$(V^{\natural})$.
