  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
$M_\textrm{gas}\sim2\times10^{11}$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.
