Using the Atacama Large Millimeter/submillimeter Array, we have detected CO(3minus2) line and far-infrared continuum emission from a galaxy associated with a high-metallicity ([M/H] = minus0.27) damped Ly$ absorber (DLA) at z $_DLA$ = 2.19289. The galaxy is located 3.Prime5 away from the quasar sightline, corresponding to a large impact parameter of 30 kpc at the DLA redshift. We use archival Very Large Telescope-SINFONI data to detect H$ emission from the associated galaxy, and find that the object is dusty, with a dust-corrected star formation rate of $$110$$$_-30$$^+60$ M$_⊙$ yr$^‑1$. The galaxyrsquos molecular mass is large, M$_mol$ = (1.4 plusmn 0.2) times 10$^11$ times ($ $_CO$/4.3) times (0.57/r $_31$) M $_⊙$, supporting the hypothesis that high-metallicity DLAs arise predominantly near massive galaxies. The excellent agreement in redshift between the CO(3ndash2) line emission and low-ion metal absorption (sim40 km s$^‑1$) disfavors scenarios whereby the gas probed by the DLA shows bulk motion around the galaxy. We use Giant Metrewave Radio Telescope H I 21 cm absorption spectroscopy to find that the H I along the DLA sightline must be warm, with a stringent lower limit on the spin temperature of T $_s$ $ 1895 times (f/0.93) K. The detection of C I absorption in the DLA, however, also indicates the presence of cold neutral gas. To reconcile these results requires that the cold components in the DLA contribute little to the H I column density, yet contain roughly 50% of the metals of the absorber, underlining the complex multi-phase nature of the gas surrounding high-z galaxies.