The compact radio source TXS 2013+370 is a $\gamma$-ray blazar which is located at a redshift of z = 0.859 at a galactic latitude b = 1.2$^o$. We observed the source with Very Long Baseline Interferometry (VLBI) at 15, 43 and 86 GHz and studied morphology and the kinematic properties of the jet. The VLBI data were then combined with flux density variability measurements at 15 and 235 GHz and with the available $\gamma$-ray light curve in the period 2008-2017. A cross-correlation analysis was performed to investigate the existence of a correlation between the variability observed in the different bands. The preliminary results of our study showed that the most prominent flares and maxima stem from the central VLBI region and most likely are associated with the nuclear region, namely the core, indicating that the activity caused by the passage of traveling shocks through the core region. In the course of our analysis, we present for the first time an 86 GHz Global Millimeter VLBI Array (GMVA) image of the innermost jet region.