  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
$1.1\pm0.2~M_{\odot}~pc^{-2}$ and the molecular gas mass lies between the
limits $4.9\times10^{8}$ to $8.3\times10^{8}~M_{\odot}$. 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.
