We report on experimental results obtained from collisions of slow highly charged Ar9+ ions with a carbon monoxide dimer (CO)2 target. A COLTRIMS setup and a Coulomb explosion imaging approach are used to reconstruct the structure of the CO dimers. The three dimensional structure is deduced from the 2-body and 3-body dissociation channels from which both the intermolecular bond length and the relative orientation of the two molecules are determined. For the 3-body channels, the experimental data are interpreted with the help of a classical model in which the trajectories of the three emitted fragments are numerically integrated. We measured the equilibrium intermolecular distance to be Re = 4.2 A. The orientation of both CO molecules with respect to the dimer axis is found to be quasi-isotropic due to the large vibrational temperature of the gas jet.