We used the Plateau De Bure Interferometer to observe multiple CO and neutral carbon transitions in a z = 2.2 main sequence disk galaxy, BX610. Our observation of CO(7-6), CO(4-3), and both far-infrared (FIR) [CI] lines complements previous observations of H alpha and low-J CO, and reveals a galaxy that is vigorously forming stars with UV fields (Log(G G(0)(-1)) less than or similar to 3.25); although less vigorously than local ultra-luminous infrared galaxies or most starbursting submillimeter galaxies in the early universe. Our observations allow new independent estimates of the cold gas mass which indicate M-gas similar to 2 x 10(11) M-circle dot, and suggest a modestly larger alpha(CO) value of similar to 8.2. The corresponding gas depletion timescale is similar to 1.5 Gyr. In addition to gas of modest density (Log(n cm(3)) less than or similar to 3) heated by star formation, BX610 shows evidence for a significant second gas component responsible for the strong high-J CO emission. This second component might either be a high-density molecular gas component heated by star formation in a typical photodissociation region, or could be molecular gas excited by low-velocity C shocks. The CO(7-6)-to-FIR luminosity ratio we observe is significantly higher than typical star-forming galaxies and suggests that CO(7-6) is not a reliable star-formation tracer in this galaxy.