The goal of the Gemini Deep Deep Survey ( GDDS ) is to study an unbiased sample of K < 20.6 galaxies in the redshift range 0.8 < z < 2.0 . Here we determine the statistical properties of the heavy element enrichment in the interstellar medium ( ISM ) of a subsample of 13 galaxies with 1.34 < z < 1.97 and UV absolute magnitude M _ { 2000 } < -19.65 . The sample contains 38 % of the total number of identified galaxies in the first two fields of the survey with z > 1.3 . The selected objects have colors typical of irregular and Sbc galaxies . Strong [ \ion O2 ] emission indicates high star formation activity in the \ion H2 regions ( SFR \sim 13 - 106 M _ { \odot } yr ^ { -1 } ) . The high S/N composite spectrum shows strong ISM \ion Mg2 and \ion Fe2 absorption , together with weak \ion Mn2 and \ion Mg1 lines . The \ion Fe2 column density , derived using the curve of growth analysis , is \log N _ { FeII } = 15.54 ^ { +0.23 } _ { -0.13 } . This is considerably larger than typical values found in damped Ly \alpha systems ( DLAs ) along QSO sight lines , where only 10 out of 87 ( \sim 11 % ) have \log N _ { FeII } \geq 15.2 . High \ion Fe2 column densities are observed in the z = 2.72 Lyman break galaxy cB58 ( \log N _ { FeII } \simeq 15.25 ) and in gamma–ray burst host galaxies ( \log N _ { FeII } \sim 14.8 - 15.9 ) . Given our measured \ion Fe2 column density and assuming a moderate iron dust depletion ( \delta _ { Fe } \sim 1 dex ) , we derive an optical dust extinction A _ { V } \sim 0.6 . If the \ion H1 column density is \log N _ { HI } < 21.7 ( as in 98 % of DLAs ) , then the mean metallicity is Z / Z _ { \odot } > 0.2 . The high completeness of the GDDS sample implies that these results are typical of star–forming galaxies in the 1 < z < 2 redshift range , an epoch which has heretofore been particularly challenging for observational programs .