We present a study of the { Mg II } absorption system at z = 0.558 towards the BL Lac object PKS 0118–272 based on high resolution spectra ( \lambda / \Delta \lambda \simeq 2 \times 10 ^ { 4 } ) obtained at the 3.6m ESO telescope and on direct imaging data obtained at the 3.5m ESO New Technology Telescope . At the redshift of the absorber we detect lines of the low ionization species { Mg I } , { Mg II } , { Ca II } , { Ti II } , { Mn II } , and { Fe II } . Most of the lines are unsaturated and we determine accurate column densities for all the species but { Mg II } . The derived column densities are typical of the interstellar gas in the disk of the Galaxy . By assuming dust-free gas with solar abundances these column densities yield N ( { HI } ) > 2.5 \times 10 ^ { 19 } cm ^ { -2 } ; however , the relative elemental abundances suggest that some dust is present and that N ( { HI } ) \simeq 2 \times 10 ^ { 20 } cm ^ { -2 } . The inferred { HI } column density indicates that the absorber is a Damped Ly \alpha system . We find [ Ti/Fe ] = +0.3 , in agreement with [ Ti/Fe ] measurements in DLA absorbers , but [ Mn/Fe ] = +0.4 , at variance with the values [ Mn/Fe ] < 0 common to DLA systems . The measured [ Ti/Fe ] and [ Mn/Fe ] ratios match remarkably well the differential depletion pattern of low-density interstellar clouds in the Galaxy . Unlike high-redshift DLA systems ( z \geq 2 ) , the z =0.558 absorber seems to originate in a galaxy that has already attained the abundances and dust content of present-day disk galaxies . The analysis of our imaging data lends support to the presence of an intervening galaxy . After a careful subtraction of the BL Lac image , an object at 1.6 ^ { \prime \prime } from PKS 0118–272 is detected . At the absorber redshift the projected distance of this close companion ( 14 h _ { 50 } ^ { -1 } kpc ) and its absolute magnitude ( M _ { R } \approx –22.3 ) are consistent with those found for galaxies associated with low-redshift DLA systems .