The nearby system 4C12.50, also known as IRAS 13451+1217 and PKS 1345+12, is a merger of gas-rich galaxies with infrared and radio activity. It has a perturbed interstellar medium (ISM) and a dense configuration of gas and dust around the nucleus. The radio emission at small (~100pc) and large (~100kpc) scales, as well as the large X-ray cavity in which the system is embedded, are indicative of a jet that could have affected the ISM. We carried out observations of the CO(1-0), (3-2), and (4-3) lines with the Atacama Large Millimeter Array (ALMA) to determine basic properties (i.e., extent, mass, and excitation) of the cold molecular gas in this system, including its already-known wind. The CO emission reveals the presence of gaseous streams related to the merger, which result in a small (4kpc-wide) disk around the western nucleus. The disk reaches a rotational velocity of 200km/s, and has a mass of 3.8(+/-0.4)10^9^M_{sun}_. It is truncated at a gaseous ridge north of the nucleus that is bright in [OIII]. Regions with high-velocity CO emission are seen at signal-to-noise ratios of between 3 and 5 along filaments that radially extend from the nucleus to the ridge and that are bright in [O iii] and stellar emission. A tentative wind detection is also reported in the nucleus and in the disk. The molecular gas speed could be as high as 2200km/s and the total wind mass could be as high as 1.5(+/-0.1)10^9^M_{sun}_. Energetically, it is possible that the jet, assisted by the radiation pressure of the active nucleus or the stars, accelerated clouds inside an expanding bubble.