Our goal is to see if there is molecular gas extending throughout the optical low surface brightness disk of the galaxy Malin 2. We used the heterodyne receiver array (HERA) mounted on the IRAM 30m telecope to make deep observations at the frequency of the CO(2--1) line at nine different positions of Malin~2. With a total observing time of 11 hours at a velocity resolution of 11 km/s we achieve a sensitivity level of ~1 mK. We detect CO(2-1) line emission from Malin~2. The line is detected in four of the nine HERA beams; a fifth beam shows a marginal detection. These results not only confirm that there is molecular gas in the disk of Malin 2, but they also show that it is spread throughout the inner 34~kpc radius as sampled by the observations of the galaxy disk. The mean molecular gas surface density in the disk is $1.1pm0.2~M_{odot}~pc^{-2}$ and the molecular gas mass lies between the limits $4.9times10^{8}$ to $8.3times10^{8}~M_{odot}$. The observed velocity dispersion of the molecular gas is higher ($sim 13$,km,s$^{-1}$) than in star forming galactic disks. This could explain the disk stability and its low star formation activity.
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