Towards practical realization of brain-inspired computing in a scalable physical system, we investigate a network of coupled micromechanical oscillators. We numerically simulate this array of all-to-all coupled nonlinear oscillators in the presence of stochasticity and demonstrate its ability to synchronize and store information in the relative phase differences at synchronization. Sensitivity of behavior to coupling strength, frequency distribution, nonlinearity strength, and noise amplitude is investigated. Our results demonstrate that neurocomputing in a physically realistic network of micromechanical oscillators with silicon-based fabrication process can be robust against noise sources and fabrication process variations. This opens up tantalizing prospects for hardware realization of a low-power brain-inspired computing architecture that captures complexity on a scalable manufacturing platform.