The generator matrix 1 0 0 0 1 1 1 0 1 1 1 X X 1 X 1 1 1 1 0 1 X 1 1 0 0 0 1 0 X 1 1 1 X 1 X X X X X 0 X 1 X 1 1 1 0 1 X 1 0 1 1 1 0 1 X 1 0 X 0 1 X 1 1 1 1 X 0 1 1 0 X 1 1 0 1 1 0 1 1 1 0 1 1 1 X 0 0 1 0 0 0 1 1 1 X 0 X+1 1 1 X+1 X 0 X 1 X 0 1 1 0 X+1 0 1 0 0 1 1 0 X+1 1 X X 1 1 1 1 0 X X 0 1 1 X+1 0 X X 1 1 1 X 0 X 1 1 1 X 1 1 1 X 1 X+1 X X+1 X 1 1 1 X 1 1 1 0 1 X 1 1 X+1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 X+1 X 0 1 1 1 X 0 1 X+1 X 1 X+1 1 X 1 0 1 X+1 X+1 1 0 0 1 1 0 X 1 0 X 1 X X X+1 0 0 0 X+1 1 1 1 X+1 0 X 0 0 1 1 X 0 X 1 X X X+1 1 0 X 0 X 1 1 1 X+1 1 X X+1 1 0 1 X X+1 0 X X X X+1 0 1 0 0 0 0 1 1 0 1 1 1 0 X X+1 0 X+1 1 X+1 X X 0 1 X+1 1 X+1 1 0 X+1 1 0 1 0 X+1 0 0 X+1 X X X 0 X 0 1 1 X+1 1 X 0 X 1 1 1 X+1 0 0 1 1 0 0 1 X X+1 X X X X+1 0 1 1 X 1 0 0 1 0 X+1 X X 0 X X+1 1 X+1 1 1 X+1 1 X+1 0 X+1 0 0 0 0 0 X 0 0 0 0 X 0 X 0 X 0 X 0 X X X 0 X 0 0 0 0 0 X 0 X 0 X X 0 X 0 X 0 0 0 0 X X 0 X 0 0 X 0 X X X 0 X X X X X 0 X X X X 0 0 0 0 X 0 X 0 0 X 0 X 0 0 0 X 0 X X 0 0 X X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X X X 0 X 0 0 X 0 0 0 X X 0 0 X 0 X X X X X 0 0 0 X X 0 0 X 0 X X X 0 0 0 X X 0 0 X 0 0 X X 0 0 X X 0 0 0 0 0 X X X X X X X 0 X 0 0 0 X 0 X 0 0 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 X X 0 X X 0 0 X X 0 X X X X 0 0 X 0 X X X 0 X X 0 X 0 0 0 X 0 X X 0 X X X 0 0 0 0 0 X 0 0 0 0 X X X X X 0 X 0 0 X X 0 0 0 X X 0 X 0 X X X X X X 0 0 0 0 0 0 0 X 0 0 0 X X 0 0 0 X X X 0 0 X X X X 0 0 0 X 0 X 0 0 X 0 X 0 0 0 X 0 0 X X X 0 0 X X X 0 X 0 0 0 X X X X X 0 0 X 0 0 X X X 0 0 0 X X 0 0 X X 0 X X X X 0 X 0 X X 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+124x^78+318x^80+399x^82+454x^84+439x^86+446x^88+409x^90+363x^92+339x^94+269x^96+227x^98+138x^100+84x^102+52x^104+21x^106+5x^108+5x^110+2x^112+1x^118 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 3.67 seconds.