The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 X 1 1 a*X 1 1 1 1 1 0 1 1 a*X 1 1 1 1 a^2*X 1 1 1 a^2*X 1 1 1 1 1 1 a*X X a*X 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 a a^2 0 a^2*X+1 a^2*X+a^2 a 1 0 a^2*X+1 a 1 a^2*X+a^2 X a^2*X+a^2 X+a a^2*X+1 1 a^2*X+a^2 a 1 0 a*X+a a*X+a^2 a^2*X+1 a*X+1 1 a^2*X a*X+1 1 X+a 0 a*X+a^2 a*X+1 1 a*X+a a*X+1 a*X+1 1 X+a^2 a^2 X+1 a^2*X X+a^2 X+a^2 1 1 1 X+1 a*X+a^2 a^2*X+1 a*X a*X+a^2 1 1 X+a X+a a*X+1 a^2*X+a^2 0 a*X+1 a*X a^2 X+a^2 1 a*X a^2*X+1 a^2*X+1 a*X+a^2 a a^2*X+a X+a a^2*X+a^2 0 a*X+a a*X 0 0 0 a^2*X 0 0 0 X X X X X X a^2*X a^2*X a*X X a*X a^2*X a^2*X 0 a^2*X a^2*X a*X a^2*X a*X 0 a*X X X a^2*X a*X a^2*X 0 a^2*X a*X 0 a*X a*X X a*X a^2*X a^2*X X X X a^2*X X X 0 X a*X a*X a*X a*X a*X a^2*X 0 a*X X a^2*X a*X X 0 a*X 0 a*X a^2*X 0 a^2*X a^2*X X 0 a*X a^2*X 0 X a*X X 0 0 0 0 X 0 X a^2*X 0 X a^2*X X 0 a*X a^2*X 0 a^2*X 0 0 a*X a*X X X a^2*X a^2*X 0 a*X a*X 0 a^2*X X X a*X X X 0 X a^2*X X 0 X X a*X a*X X 0 a^2*X X a*X a*X 0 a*X a*X 0 X a^2*X a*X a*X a^2*X a*X 0 a*X 0 X a*X 0 X a^2*X 0 X a*X a*X 0 a^2*X a^2*X X X a*X a^2*X 0 0 0 0 0 a^2*X a^2*X X a^2*X a*X 0 a^2*X X X a*X X a*X a*X X a^2*X a^2*X 0 a^2*X a^2*X X 0 a^2*X 0 a^2*X a^2*X a*X X X a*X X a^2*X X 0 a*X a*X 0 a*X 0 X X a*X a*X a^2*X X 0 0 a*X a*X a*X X 0 a*X X a^2*X X a*X a^2*X 0 a*X 0 a*X a*X a^2*X a^2*X 0 0 a*X X X X 0 X a*X 0 X generates a code of length 79 over F4[X]/(X^2) who´s minimum homogenous weight is 220. Homogenous weight enumerator: w(x)=1x^0+60x^220+240x^223+507x^224+300x^226+684x^227+981x^228+456x^230+864x^231+1155x^232+552x^234+1260x^235+1341x^236+624x^238+1152x^239+1188x^240+732x^242+1140x^243+960x^244+360x^246+624x^247+729x^248+48x^250+180x^251+87x^252+57x^256+39x^260+15x^264+18x^268+9x^272+6x^276+3x^280+12x^284 The gray image is a linear code over GF(4) with n=316, k=7 and d=220. This code was found by Heurico 1.16 in 1.82 seconds.