The generator matrix 1 0 0 0 0 0 0 1 1 1 0 1 X 1 1 0 1 0 X X 1 1 1 1 1 1 1 0 X X 1 0 0 X 0 1 1 0 1 1 X X 0 0 X 0 1 X 0 1 1 0 X 0 X X 1 0 1 1 1 1 1 1 X X 1 1 1 1 1 0 X 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X 1 1 1 1 X+1 X+1 X+1 1 1 X+1 0 1 1 X 1 1 1 X X+1 X+1 1 0 X 1 X 1 1 1 1 1 1 0 X X+1 1 0 0 1 X 1 0 X+1 0 1 X X+1 X 1 0 0 X+1 1 X 0 1 X 0 1 1 1 1 X+1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 X X X X X X 0 X 0 X 0 0 X X+1 1 1 X+1 1 X+1 1 1 X+1 1 1 X+1 X+1 1 X+1 1 1 1 1 X+1 1 X+1 1 0 X X+1 X+1 X+1 X+1 X+1 0 1 X+1 1 X+1 1 0 X X 0 1 X+1 X X 0 0 1 0 0 0 1 0 0 0 0 0 X X 1 1 X+1 X+1 1 1 1 X+1 X X 1 X+1 X X 1 X+1 1 X+1 X 0 X+1 X 0 X X 0 1 X 1 X 1 0 0 X X+1 0 X+1 1 0 1 X 0 X+1 1 X X X X+1 1 1 0 0 X+1 X 1 0 0 0 0 X 1 1 X X 0 1 X 1 X+1 X+1 1 0 0 0 0 1 0 0 X 1 X+1 1 0 1 1 1 X+1 X X+1 0 0 X X 0 X 1 1 1 0 X X+1 0 X+1 1 0 X X+1 X+1 1 0 1 0 X+1 X 0 1 X 0 X X X+1 X+1 X 1 X 0 X+1 X 1 X+1 X 1 1 X 1 X X X+1 1 X+1 0 1 X X+1 1 0 X X 1 X X 1 0 0 0 0 0 0 1 0 X+1 1 0 1 X X+1 X+1 0 X X+1 1 X+1 1 X+1 1 X X 0 1 0 X+1 X 1 X+1 X+1 X 0 X 1 0 0 X+1 1 X+1 X+1 X X+1 1 1 X 0 X 0 X 1 X+1 1 X 0 1 X 1 X X+1 1 1 X+1 1 X 1 X+1 X+1 1 0 X+1 X+1 1 1 0 X X+1 1 0 1 0 0 0 0 0 0 0 1 1 X 1 1 X+1 X 1 X 1 X X+1 X X+1 X X+1 0 1 X 0 X+1 1 X+1 0 1 1 X+1 X 1 X X+1 1 X X 0 1 1 0 1 X+1 0 0 1 X X X X 0 X 1 0 0 X+1 0 0 X 0 X+1 X+1 X+1 0 1 X 1 X+1 X+1 0 0 1 X 1 X 1 X+1 X 0 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+61x^68+134x^69+218x^70+322x^71+374x^72+532x^73+644x^74+622x^75+664x^76+760x^77+769x^78+848x^79+909x^80+894x^81+949x^82+884x^83+909x^84+852x^85+788x^86+792x^87+696x^88+632x^89+502x^90+466x^91+378x^92+236x^93+189x^94+148x^95+100x^96+50x^97+32x^98+12x^99+4x^100+2x^101+4x^102+2x^103+4x^105+1x^130 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 98.1 seconds.