Nowadays, the demand for medical image computing is exceptionally high. This growth was mostly driven by the manual development of machine learning models, in particular neural networks. However, due to the constant evolution of domain requirements, manual model development has become insufficient. The present study proposes a heuristic architecture search that can be in an excellent service for the task of medical image classification. We implemented a novel approach called network morphism to the search algorithm. The proposed search method utilizes the enforced hill-climbing algorithm and functional-saving modifications. As a result of computational experiments, the search method found the optimal architecture in 28 GPU hours. The model formed by the found architecture achieved performance of 73.2% in validation accuracy and 84.5% in AUC on the validation dataset that is competitive to the state-of-the-art hand-crafted networks. Moreover, the proposed search method managed to find the architecture that contains four times fewer parameters. Besides, the model requires almost ten times less physical memory, which may indicate the practical usefulness of our method in medical image analysis.