In the present paper, we describe a spiking neural network (SNN) architecture CoLaNET which can be used in wide range of supervised learning classification tasks. It is assumed, that all participating signals (the classified object description, correct class label and SNN decision) have spiking nature. The distinctive feature of this architecture is a combination of prototypical network structures corresponding to different classes and significantly distinctive instances of one class (=columns) and functionally differing populations of neurons inside columns (=layers). The other distinctive feature is a novel combination of anti-Hebbian and dopamine-modulated plasticity. The plasticity rules are local and do not use the backpropagation principle. Besides that, we were guided by the requirement that the all neuron/plasticity models should be easily implemented on modern neurochips. We illustrate the high performance of CoLaNET on two classification tasks of very different kinds – MNIST dataset, and a task related to model-based reinforcement learning, namely, evaluation of proximity of an external world state to the target state.