The generator matrix 1 0 0 0 0 0 1 1 1 1 0 1 0 X 1 1 0 1 X 1 1 1 1 X 1 0 X 1 0 1 X 1 X X X 1 1 1 1 X 0 1 X X 0 0 0 1 0 0 1 X 0 X 1 1 0 1 1 1 0 0 1 1 1 1 X 1 0 0 X 1 1 0 1 1 1 1 X 1 X 1 0 1 X 0 X 1 1 0 1 0 0 0 0 X X 1 X 1 1 0 1 X+1 1 1 X 1 1 X+1 X+1 0 1 X X X X X 1 1 X+1 1 X 0 0 X+1 0 1 0 X 0 1 1 1 1 0 1 1 X X+1 X 0 1 0 0 1 0 X 1 1 X X+1 0 X+1 1 1 X+1 0 1 1 0 0 1 X X X 0 0 0 X 0 1 X X 1 0 X 0 0 0 1 0 0 0 0 0 0 0 0 X X X X 0 1 X+1 1 X+1 1 X+1 1 1 X+1 1 1 X+1 1 1 1 0 X 1 1 X 0 0 1 0 0 X+1 X+1 X 1 X+1 X 0 X+1 0 1 X 1 X+1 X 1 X+1 1 0 1 X 1 X+1 1 0 0 X+1 0 X X X 0 1 1 X+1 X 0 0 1 X 1 X X 0 1 1 1 X+1 0 0 0 0 1 0 0 0 0 0 X X X 0 X 0 X X 0 X 0 X 0 X X X X X X X X 0 1 1 1 1 X+1 X+1 X+1 X+1 1 1 1 X+1 1 X+1 X+1 1 1 1 1 X+1 X X+1 X+1 X X+1 X 1 1 0 1 0 X 1 X X+1 X X+1 X 1 1 X+1 0 X 0 X 0 X+1 X+1 X+1 X 1 X+1 1 X+1 1 1 0 0 0 0 0 0 1 0 0 X+1 X X+1 1 X+1 1 X+1 1 0 0 1 X 1 0 X+1 0 X+1 X+1 1 0 X X+1 X 1 X+1 X X+1 0 1 1 X 1 X+1 0 1 X+1 X+1 X+1 0 X X 0 X+1 X+1 X 1 1 0 X X+1 X+1 1 X 0 X X 1 X 0 1 X+1 X 1 1 X 1 1 X X+1 0 0 X+1 X+1 1 1 0 0 X X+1 X 0 0 0 0 0 0 0 1 1 X+1 1 0 1 0 1 X X+1 X X+1 X 0 0 0 1 1 1 1 X 1 X 1 X+1 X X 1 X+1 0 X 1 X 1 1 1 X X+1 X+1 0 1 X 0 0 X 0 1 X 0 X+1 0 1 X+1 0 0 X 0 1 1 0 X+1 1 X 1 1 X X+1 0 0 1 X+1 X 0 0 1 1 1 0 1 0 1 0 X 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+50x^78+106x^79+153x^80+204x^81+235x^82+226x^83+228x^84+242x^85+235x^86+232x^87+196x^88+208x^89+174x^90+186x^91+200x^92+164x^93+150x^94+132x^95+156x^96+134x^97+105x^98+94x^99+64x^100+56x^101+61x^102+42x^103+22x^104+14x^105+14x^106+4x^107+4x^108+2x^109+2x^115 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 3.31 seconds.