Single-photon emission computed tomography (SPECT) is a well known imaging method of nuclear medicine, which allows obtaining tomographic images of the biodistribution of radiolabeled compounds, both throughout the patient’s body and in separate organs. At the same time, a small animal SPECT is currently a key tool in the development of new radiopharmaceuticals and to seek for methods for their targeted delivery. However, in studies of small animals, the region of interest typically has a small size and a high spatial resolution is necessary to get a good image. A system based on the coded aperture and the hybrid pixel Timepix detector with the CdTe sensor is developed as a possible imaging solution for the small animal SPECT. Characterization of the system using an X-ray source and various radioactive gamma emitters, including Tc-99m and I-125, is made. The spatial resolution is shown to be of 0.8-0.9 mm at the field of view of 3 cm x 3 cm for the energy range typical for SPECT. The experimental data, supported by the simulation, confirm that a 1 mm thick tungsten coded aperture is sufficient to obtain an image of the distributed radioactive sources with the energy of gamma rays at least up to 180 keV without significant reconstruction artifacts. The reconstructed tomographic images of a SPECT phantom are presented.