Molecular photofragmentation has been studied by event imaging on HeH+ ions at 32 nm (38.7 eV) in a fast ion beam crossed with the free-electron laser in Hamburg (FLASH), analyzing neutral He product directions and energies. Fragmentation into He(1snl,n > or = 2)+H+ was observed to yield significant photodissociation at 32 nm with an absolute cross section of (1.4+/-0.7) x 10(-18) cm2, releasing energies of 10-20 eV. A clear dominance of photodissociation perpendicular to the laser polarization was found in contrast to the excitation paths so far emphasized in theoretical studies.