Neuromorphic systems using memristive devices provide a brain-inspired alternative to the classical von Neumann processor architecture. In this work, a spiking neural network (SNN) implemented using phase-change synapses is studied. The network is equipped with a winner-take-all (WTA) mechanism and a spike-timing-dependent synaptic plasticity rule realized using crystal-growth dynamics of phase-change memristors. We explore various configurations of the synapse implementation and we demonstrate the capabilities of the phase-change-based SNN as a pattern classifier using unsupervised learning. Furthermore, we enhance the performance of the SNN by introducing an input encoding scheme that encodes information from both the original and the complementary pattern. Simulation and experimental results of the phase-change-based SNN demonstrate the learning accuracies on the MNIST handwritten digits benchmark.