We consider an implementation of convolutional architecture in a spiking neural network (SNN) used to classify images. As in the traditional neural network, the convolutional layers form informational "features" used as predictors in the SNN-based classifier with CoLaNET architecture. Since weight sharing contradicts the synaptic plasticity locality principle, the convolutional weights are fixed in our approach. We describe a methodology for their determination from a representative set of images from the same domain as the classified ones. We illustrate and test our approach on a classification task from the NEOVISION2 benchmark.