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(G G₀⁻¹ ) ≲ 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 M_gas ∼ 2 × 10¹¹ M_⊙, and suggest a modestly larger α_CO 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.