  The phase diagram of a model describing doped CuGeO$_3$ is derived. The model
emphasizes the role of local moments released by the impurities and randomly
distributed inside the gaped singlet background. The phase diagram is
investigated by two methods: (i) in a mean field treatment of the interchain
coupling and (ii) in a real space decimation procedure in a two dimensional
model of randomly distributed moments. Both methods lead to similar results, in
a qualitative agreement with experiments. In particular, a transition to an
inhomogeneous N\'eel phase is obtained for arbitrary small doping. From the
decimation procedure, we interpret this phase at very low doping as a {\sl
Griffith antiferromagnet}. Namely, it does not have a true long range order
down to zero temperature. Nonetheless, large magnetically ordered clusters
appear already at relatively high temperatures. This demonstrates the role of
disorder in the theoretical description of doping in CuGeO$_3$. A detailed
comparison with other approaches is also given.
