Context. Relativistic jets in active galactic nuclei are one of the most powerful phenomena in the Universe. They form in the surroundings of the supermassive black holes as a by-product of accretion onto the central black hole in active galaxies. The flow in the jets propagates at velocities close to the speed of light. The distance between the first part of the jet that is visible in radio images (core) and the black hole is still a matter of debate. Aims. Only very-long-baseline interferometry observations resolve the innermost compact regions of the radio jet. These observations can access the jet base, and by combining data at different wavelenghts, address the physical parameters of the outflow from its emission. Methods. We have performed an accurate analysis of the frequency-dependent shift of the VLBI core location for a multi-wavelength set of images of the blazar CTA 102 including data from 6 cm down to 3 mm. Results. The measure of the position of the central black hole, with mass ~10^8.93M_⊙, in the blazar CTA 102 reveals a distance of ~8 × 10^4 gravitational radii to the 86 GHz core, in agreement with similar measures obtained for other blazars and distant radio galaxies, and in contrast with recent results for the case of nearby radio galaxies, which show distances between the black hole and the radio core that can be two orders of magnitude smaller.