Ba2Co2+ 3Co3+ 6O14 has been prepared by conventional solid-state reaction between BaO2 and CoO. Its crystal structure has been refined from single-crystal X-ray diffraction data and powder neutron diffraction, a = 5.6963(8) Å, c = 28.924(6) Å, space group R3̄m, Z = 3, R1 = 4.44%, wR2 = 10.96%. It shows evidence of new building blocks called T‘ (ch‘h‘c stacking sequence of cubic O4 and hexagonal BaO3 layers) by analogy with the related T-blocks (hh‘h‘h) of the barium hexaferrites. T‘ consists of CoII,IIIO2 brucite-like layers pillared by CoIIO4 tetrahedra and CoIII 3O12 octahedral trimers. Below T N = 39 K, tetrahedral and octahedral high spin CoII (S = 3/2) diluted in the framework mainly containing low spin CoIII (S = 0) interact through CoII−O−O−CoII through super-super exchanges (SSE) only. The analysis of the competition between the multiple SSE paths has been performed through geometrical considerations. The magnetic moments are lying antiferromagnetically in the a,b plane in good agreement with the magnetic group theory presented in our work. Their values of 1.70(4) μB and 2.83(3) μB for the octahedral and tetrahedral CoII, respectively, are explained by the high degree of covalency and magnetic transfer toward the surrounding anions involved in the SSEs. At high temperature, the creation of oxygen vacancies is observed and strongly intervenes in the hopping conductivity as shown from the abrupt change in the matching Arrhenius law. This particular feature demonstrates potential mixed conductivity processes in the medium-temperature range. At 1000 °C, it reversibly decomposes into CoO and BaCoO3- δ. Finally, the medium crystallinity of the title compound is explained by the presence of defects and intergrowths with other hexagonal perovskites of the Ba−Co−O system.