Galaxy halos appear to be missing a large fraction of their baryons, most probably hiding in the circumgalactic medium (CGM), a diffuse component within the dark matter halo that extends far from the inner regions of the galaxies. A powerful tool to study the CGM gas is offered by absorption lines in the spectra of background quasars. Here, we present optical (MUSE) and mm (ALMA) observations of the field of the quasar Q1130-1449 which includes a log [N(HI)/cm^-2]=21.71±0.07 absorber at z=0.313. Ground-based VLT/MUSE 3D spectroscopy shows 11 galaxies at the redshift of the absorber down to a limiting SFR>0.01 M_☉yr^-1 (covering emission lines of [O II], Hβ, [O III], [N II] and Hα), 7 of which are new discoveries. In particular, we report a new emitter with a smaller impact parameter to the quasar line-of-sight (b=10.6 kpc) than the galaxies detected so far. Three of the objects are also detected in CO(1-0) in our ALMA observations indicating long depletion timescales for the molecular gas and kinematics consistent with the ionised gas. We infer from dedicated numerical cosmological RAMSES zoom-in simulations that the physical properties of these objects qualitatively resemble a small group environment, possibly part of a filamentary structure. Based on metallicity and velocity arguments, we conclude that the neutral gas traced in absorption is only partly related to these emitting galaxies while a larger fraction is likely the signature of gas with surface brightness almost four orders of magnitude fainter that current detection limits. Together, these findings challenge a picture where strong-N(H I) quasar absorbers are associated with a single bright galaxy and favour a scenario where the H I gas probed in absorption is related to far more complex galaxy structures....