The generator matrix 1 0 0 0 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2a+2 1 1 1 0 1 1 2a 2a 0 0 1 1 1 1 2 1 1 1 1 1 1 1 2a 0 1 1 1 1 0 1 1 2 2a 1 1 1 2a+2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2a+2 1 0 1 0 0 0 2 2 2a+3 2a+1 1 3a 3a+3 a+2 a+3 a+1 2a 3a 2a+2 2a 2a+1 a+3 2a+1 1 3 3a+1 3a+2 1 3a+2 2a+3 1 1 2 1 a+3 3a 3a+3 2a 2a 2a 3 1 3a+2 3a+2 a 3a+2 2a 1 3a+1 a+3 2a+1 3a 1 2 a+3 1 1 0 a+3 0 1 a a+3 a+2 2a+3 3a+3 2 2a+3 3a 1 3a a+3 2a+3 3a+1 a+1 1 2a+1 1 2 0 0 1 0 1 3a+2 a+1 a 2a+2 3a+2 2a+3 3a+1 a 3a+2 3a+3 0 3a 3a+3 a a+3 0 1 3a+1 3a 2a+1 a+2 1 1 2a+3 2 a+2 1 3 2a+3 2a+2 a 2a+1 1 2a+1 3a 2a+3 2 3a+1 2a+1 0 1 3a+1 3 3a+2 0 3a+1 3a+2 0 2a+2 a+2 2a+3 3 2 3a+1 2a+2 a+3 3a+1 0 3a+2 2a+1 a+3 2a+3 2 a+3 a+1 2a 3 2 3a+3 a 3a+2 a+3 2a+3 0 0 0 1 3a+3 a 1 2 a+2 a+2 0 2 3a+1 2a+3 3a+1 a+2 0 2 a+3 a 3a+1 3 2a+2 2a+1 a+2 2a+1 a 3a+3 3a+2 1 3 3a+1 2a 2a+1 3 a+1 3a+2 2a+3 2a 3 a+1 3a+1 3a 3a a+2 3a+2 3a+2 2a+2 2a+2 3a+1 2a+3 2a a+3 1 2a+1 a+1 3a+1 3a+2 1 a 3a+3 2a+1 2a+2 2a+1 0 3a+2 3a+1 2a+1 a+1 0 0 a 2a+1 3 2a+2 3a 0 a+3 0 0 0 0 2 0 2a 0 0 0 2 2a 2 2a 2 2a 2a+2 2a+2 2a+2 2a 0 0 2a 2 0 2a 2a 2a+2 2 2 0 2 0 2a+2 0 2a 2 2a 0 2a+2 2a+2 2a 2 2a+2 2 2 2a+2 2 2a+2 2 2a+2 2 2a+2 2a 2 2a 0 2a 0 2a 2a 0 2 0 0 0 2a 2a+2 2 2 2a+2 0 0 2a+2 2a 2a+2 2 2 generates a code of length 78 over GR(16,4) who´s minimum homogenous weight is 213. Homogenous weight enumerator: w(x)=1x^0+564x^213+288x^214+924x^215+726x^216+2892x^217+804x^218+2988x^219+1929x^220+6960x^221+2208x^222+6480x^223+3189x^224+11304x^225+3168x^226+10152x^227+4695x^228+17124x^229+4752x^230+13704x^231+6264x^232+22932x^233+6828x^234+16128x^235+7128x^236+23304x^237+6108x^238+14988x^239+5427x^240+18444x^241+4104x^242+9384x^243+3357x^244+9504x^245+1800x^246+4260x^247+1644x^248+3072x^249+648x^250+804x^251+309x^252+624x^253+12x^254+60x^255+69x^256+12x^257+33x^260+15x^264+18x^268+6x^272+3x^276+3x^280 The gray image is a code over GF(4) with n=312, k=9 and d=213. This code was found by Heurico 1.16 in 292 seconds.