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$_0^{-1}) lesssim3.25);$ 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 $M_textrm{gas}sim2times10^{11}$M$_odot$, and suggest a modestly larger $alpha_{textrm{CO}}$ value of $sim$8.2. The corresponding gas depletion timescale is $sim$1.5 Gyr. In addition to gas of modest density (Log($n$ cm$^3)lesssim3$ ) 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.
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