Context : Aims : Our goal is to see if there is molecular gas extending throughout the optical low surface brightness disk of the galaxy Malin 2 . Methods : 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 . Results : 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 1.1 \pm 0.2 ~ { } M _ { \odot } ~ { } pc ^ { -2 } and the molecular gas mass lies between the limits 4.9 \times 10 ^ { 8 } to 8.3 \times 10 ^ { 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 . Conclusions :