The generator matrix 1 0 0 0 0 0 1 1 1 0 1 1 X 1 0 1 1 X 1 1 X 0 0 1 X 1 1 1 1 0 0 X 1 X 1 X 0 1 1 1 0 0 X 0 1 X X 1 1 1 0 X 0 1 1 1 0 X 1 1 1 X 1 X X 1 X 1 X X 0 1 X 0 X 0 1 X X 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 X 1 1 1 1 X+1 1 1 1 1 X 0 X X+1 X+1 X X 1 1 1 1 1 1 X 0 X+1 0 X 0 1 X+1 1 1 0 X 1 1 1 1 X 1 1 X X 1 X+1 0 X X 1 0 X+1 1 0 1 X X X 0 0 X 1 X X 1 X 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 X+1 1 X 1 X+1 0 0 X+1 X+1 X X+1 1 X 1 1 X X 0 0 1 0 1 X+1 1 0 X 1 X 1 1 X+1 0 0 0 1 0 X X X+1 0 1 1 1 1 1 0 X+1 1 1 X 1 1 X 0 X+1 X 1 X 0 1 1 X 1 0 0 1 1 X+1 0 0 0 0 1 0 0 0 1 1 1 X 1 X+1 X+1 X+1 X 0 0 X X+1 X+1 0 1 X+1 X X 0 0 X+1 X 1 X X+1 X+1 0 X X+1 X+1 0 X X X X+1 0 X+1 X 1 X 0 X+1 0 0 0 1 1 X X X X+1 X 1 X+1 X 0 0 1 0 X X+1 X 1 X 1 1 0 X 0 1 X+1 X 0 0 0 0 0 0 1 0 1 1 0 X+1 X 0 X X+1 1 0 X+1 X+1 X+1 1 X X X 1 X+1 0 X+1 0 X 1 0 X+1 0 X+1 1 X 1 X+1 X+1 0 X X+1 1 X X+1 X+1 1 1 X X X+1 X+1 X X+1 1 X 0 X X+1 0 X 1 1 X X+1 1 X X 1 0 1 0 X X+1 1 1 X+1 0 0 X+1 0 0 0 0 0 0 0 1 1 0 X+1 X+1 1 X X+1 X+1 X 1 X+1 0 0 X+1 X 1 X+1 0 1 X X X X 0 0 X+1 1 0 1 1 1 0 X+1 X 1 X+1 0 1 1 1 X 0 0 0 1 X 0 X+1 X 0 1 1 0 1 X+1 1 0 0 0 X X+1 1 1 1 X+1 1 X+1 0 X X X+1 X X 1 0 0 0 0 0 0 0 0 X 0 X X X 0 X X 0 X X 0 0 X 0 X X 0 X 0 0 X X X X 0 0 X 0 0 X 0 X X 0 0 0 0 X 0 0 X X X X X 0 X X 0 X 0 X 0 X X X X X 0 0 0 X X 0 X 0 0 X X 0 0 X X 0 0 0 0 0 0 0 0 0 X 0 X 0 X X 0 0 0 0 0 X 0 0 X X X X X X 0 0 X X 0 X X X 0 0 0 X X X X X X X X X X X X 0 0 X X X X 0 X 0 X X 0 0 0 0 X X X X 0 0 X 0 X 0 0 0 0 X X X X generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+81x^68+112x^69+275x^70+294x^71+419x^72+464x^73+567x^74+670x^75+641x^76+760x^77+814x^78+876x^79+825x^80+934x^81+872x^82+938x^83+978x^84+908x^85+769x^86+740x^87+687x^88+648x^89+525x^90+414x^91+365x^92+236x^93+220x^94+152x^95+90x^96+34x^97+50x^98+10x^99+7x^100+1x^102+2x^103+2x^104+2x^106+1x^134 The gray image is a linear code over GF(2) with n=164, k=14 and d=68. This code was found by Heurico 1.16 in 99.8 seconds.