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 Hα and low-J CO, and reveals a galaxy that is vigorously forming stars with UV fields (Log(GG0-1) ≲ 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 Mgas ˜ 2 × 1011 M⊙, and suggest a modestly larger αCO value of ˜8.2. The corresponding gas depletion timescale is ˜1.5 Gyr. In addition to gas of modest density (Log(n cm3) ≲ 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. The reduced spectra are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/628/A104