Spiking Neural Networks (SNNs) offer an event-driven and more biologically realistic alternative to standard Artificial Neural Networks based on analog information processing. This can potentially enable energy-efficient hardware implementations of neuromorphic systems which emulate the functional units of the brain, namely, neurons and synapses. Recent demonstrations of ultra-fast photonic computing devices based on phase-change materials (PCMs) show promise of addressing limitations of electrically driven neuromorphic systems. However, scaling these standalone computing devices to a parallel in-memory computing primitive is a challenge. In this work, we utilize the optical properties of the PCM, Ge\textsubscript{2}Sb\textsubscript{2}Te\textsubscript{5} (GST), to propose a Photonic Spiking Neural Network computing primitive, comprising of a non-volatile synaptic array integrated seamlessly with previously explored `integrate-and-fire' neurons. The proposed design realizes an `in-memory' computing platform that leverages the inherent parallelism of wavelength-division-multiplexing (WDM). We show that the proposed computing platform can be used to emulate a SNN inferencing engine for image classification tasks. The proposed design not only bridges the gap between isolated computing devices and parallel large-scale implementation, but also paves the way for ultra-fast computing and localized on-chip learning.