Summary: This correspondence presents a multistage decoding approach for a free \(\mathbb Z_q\)-submodule of \(\mathbb Z_q^N\) of rank \(K\) defined by a sparse \((N-K)\times N\) parity-check matrix over \(\mathbb Z_q\) where \(q=p^m\), \(p=2\) and \(m>1\). The proposed method involves the repeated application of belief propagation decoding to exploit the natural ring epimorphism \(\mathbb Z_q\to\mathbb Z_q^l: r\mapsto \sum_{i=0}^{l-1}r^{(i)}p^i\) with kernel \(p^l\mathbb Z_q\) for each \(l\), \(1\leq\l\leq m\), where \(\sum_{i=0}^{m-1}r^{(i)}p^i\) is the \(p\)-adic expansion of \(r\). Computer simulations for codes of rate half and moderate length on an additive white Gaussian noise (AWGN) channel with various modulation schemes show that such a decoding strategy offers an additional coding gain of between 0.07--0.1 dB over a single-stage decoding approach.