The generator matrix 1 0 0 0 0 1 1 1 1 1 X 1 1 0 X 0 1 1 1 1 X 1 0 1 X X X 1 0 0 1 X 0 0 1 1 0 0 X 1 1 0 X 1 1 1 X 1 1 X X X 1 1 X 1 0 1 1 1 1 X 1 1 1 0 0 1 1 X 1 0 1 1 X 1 1 0 1 X 1 1 1 1 1 X 1 1 1 0 1 0 0 0 0 0 0 0 X 0 0 X X X X 1 1 1 X+1 1 1 1 X+1 1 1 1 0 1 1 X+1 1 1 1 1 1 0 1 0 1 X+1 0 X X 1 X 1 0 X+1 1 X 1 X+1 X 0 X+1 1 X+1 X X+1 X+1 1 X X+1 X 0 0 0 1 X 1 1 X+1 X 0 1 0 0 0 X 1 X+1 X 0 1 1 X+1 X 0 0 0 1 0 0 0 1 0 1 1 X X+1 0 1 1 1 X+1 0 X+1 X X+1 1 X 0 1 X 1 1 1 0 1 1 X X 0 0 X X+1 0 X+1 1 1 1 X 1 X 0 X+1 1 1 X X X X+1 0 1 0 0 X+1 0 X+1 X X+1 X 0 1 1 1 X 0 1 X+1 0 1 0 1 X+1 0 0 1 0 X+1 X X 0 X+1 0 1 X+1 0 0 0 1 0 1 1 X X X 1 X+1 X+1 X 1 1 X 1 1 1 0 0 X 0 0 X+1 1 X+1 1 X+1 1 1 0 0 1 X 1 X 0 X 1 X+1 X 1 0 1 X+1 1 X+1 1 1 0 1 X 1 0 1 X+1 0 0 1 X+1 0 0 0 0 X X+1 X 1 X+1 X X+1 0 1 1 1 1 1 X+1 0 0 1 1 0 X 1 X X 0 0 0 0 1 1 0 1 X+1 X X+1 X+1 0 1 0 X+1 X X+1 0 0 X X+1 1 X X+1 1 1 0 0 0 1 1 X+1 0 X+1 X+1 1 X 1 1 X+1 X X+1 X+1 0 X X+1 X+1 0 1 0 0 X X 0 X 1 1 X+1 0 X+1 X 0 X 1 0 X+1 1 X+1 X X 0 X+1 X 0 1 X X+1 0 X+1 1 1 1 X X X X 1 1 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X X X X X X 0 X 0 0 0 X X X 0 X X 0 0 X 0 X X 0 X X X 0 X 0 X X 0 0 0 0 0 X X 0 X 0 X 0 0 X X X X X X 0 X X 0 0 0 X 0 X X X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X 0 X X 0 X X 0 X X X X X X X X X X 0 X X X X 0 X X X X 0 0 0 0 X X X 0 X 0 0 X 0 0 X generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+68x^78+132x^79+147x^80+184x^81+204x^82+218x^83+233x^84+252x^85+203x^86+206x^87+208x^88+218x^89+240x^90+192x^91+180x^92+144x^93+158x^94+150x^95+147x^96+152x^97+105x^98+84x^99+74x^100+60x^101+30x^102+24x^103+29x^104+14x^105+13x^106+18x^107+5x^108+1x^110+2x^114 The gray image is a linear code over GF(2) with n=178, k=12 and d=78. This code was found by Heurico 1.16 in 3.44 seconds.