An important research topic in neuroscience is the study of mechanisms underlying memory and the estimation of the information capacity of the biological system. In this report we investigate the performance of a modular attractor network with recurrent connections similar to the cortical long-range connections extending in the horizontal direction. We considered a single learning rule, the BCPNN, which implements a kind of Hebbian learning and we trained the network with sparse random patterns. The storage capacity was measured experimentally for networks of size between 500 and 46 K units with a constant activity level, gradually diluting the connectivity. We show that the storage capacity of the modular network with patchy connectivity is comparable with the theoretical values estimated for simple associative memories and furthermore we introduce a new technique to prune the connectivity, which enhances the storage capacity up to the asymptotic value.