Here we analyze radio, optical, and X-ray data for the peculiar cluster Abell 578. This cluster is not fully relaxed and consists of two merging sub-systems. The brightest cluster galaxy (BCG), CGPG 0719.8 6704, is a pair of interacting ellipticals with projected separation ~10 kpc, the brighter of which hosts the radio source 4C 67.13. The FanaroffRiley type-II radio morphology of 4C 67.13 is unusual for central radio galaxies in local Abell clusters. Our new optical spectroscopy revealed that both nuclei of the CGPG 0719.8 6704 pair are active, albeit at low accretion rates corresponding to the Eddington ratio $\sim {{10}^{-4}}$ (for the estimated black hole masses of $\sim 3\times {{10}^{8}}\;{{M}_{\odot }}$ and $\sim {{10}^{9}}\;{{M}_{\odot }}$). The gathered X-ray (Chandra) data allowed us to confirm and to quantify robustly the previously noted elongation of the gaseous atmosphere in the dominant sub-cluster, as well as a large spatial offset (~60 kpc projected) between the position of the BCG and the cluster center inferred from the modeling of the X-ray surface brightness distribution. Detailed analysis of the brightness profiles and temperature revealed also that the cluster gas in the vicinity of 4C 67.13 is compressed (by a factor of about ~1.4) and heated (from $\simeq 2.0$ keV up to 2.7 keV), consistent with the presence of a weak shock (Mach number ~1.3) driven by the expanding jet cocoon. This would then require the jet kinetic power of the order of $\sim {{10}^{45}}$ erg s−1, implying either a very high efficiency of the jet production for the current Show Partial Abstract