The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 X 0 1 X 1 1 X 0 1 1 1 1 0 0 X 1 1 0 X 1 1 1 1 1 1 0 0 X 1 1 X 1 1 X X X 0 0 1 1 1 1 1 0 1 X 1 X 0 1 0 0 1 1 1 X 1 X 1 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 X X+1 1 0 X 1 0 1 1 X 0 1 X 1 1 1 X X 0 X+1 X 1 0 X+1 1 1 1 X+1 0 1 1 0 1 X 1 0 1 1 X 1 0 X+1 1 X+1 1 X X X X+1 1 X 0 1 X 1 1 0 1 0 X 1 X+1 1 X 1 1 X 0 0 X 0 0 0 1 1 1 0 1 0 1 1 0 X X+1 1 0 X 0 1 X+1 1 1 X 1 0 1 1 0 1 X+1 1 1 0 0 1 X+1 0 1 X+1 X 0 X 1 X 1 X 1 1 1 1 X X 0 X X+1 0 0 1 1 1 1 1 0 1 1 1 1 0 X+1 0 1 0 0 X 0 X 0 X X 0 1 1 X+1 1 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X X X 0 X X 0 X X 0 X 0 X 0 0 0 X 0 0 X X 0 X 0 X X X X 0 0 X 0 0 0 0 0 0 X X X 0 X 0 X 0 X X X 0 0 X X 0 X X X X 0 0 X X 0 0 X 0 0 X X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 X X X 0 0 0 0 0 0 X X 0 X 0 X 0 0 X 0 0 X X 0 X 0 X 0 X 0 0 X X X 0 0 0 X X X X X 0 0 0 X 0 X X 0 X X X X X 0 0 X 0 X 0 0 0 0 0 0 0 0 0 0 X 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 X X X X X X X X X X X X X X X 0 X X X X 0 X X X X 0 0 0 X 0 X X X X 0 0 0 0 X 0 X X X 0 X X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 X 0 X 0 X X 0 X X 0 X X 0 0 0 X X X 0 0 0 X X X 0 0 0 X X 0 X X X X 0 0 0 X X 0 X 0 X X 0 X 0 X 0 X 0 0 0 0 0 0 X X X X 0 0 0 0 X X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X 0 0 0 0 X 0 X 0 0 0 X 0 X X 0 X X X 0 X X X 0 0 0 X 0 X X 0 X 0 0 0 0 X 0 0 X X 0 0 X 0 0 0 X 0 0 X X X 0 X 0 X 0 X X X X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X 0 X X X X 0 X X X X X X X 0 X 0 X X X X X X X 0 X X 0 X 0 X X 0 X X X 0 X 0 X X X X X 0 X 0 X 0 0 X X 0 X 0 X 0 0 0 X X 0 0 X 0 X X 0 0 X 0 0 0 0 0 0 0 0 0 0 X 0 X X 0 X X X 0 X X 0 X X 0 X 0 X X X 0 X 0 X 0 0 X 0 0 X X 0 0 0 X X X X X 0 X 0 X 0 0 X 0 0 0 X 0 X X 0 X 0 0 X 0 0 0 0 0 0 0 X 0 X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X X X X X X X 0 0 X X X X 0 0 0 0 X X 0 X X 0 0 X 0 X 0 0 X 0 0 X X X 0 X X 0 X X X 0 0 0 0 X X X 0 0 X X X X X X 0 0 0 0 X X generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+39x^68+42x^69+139x^70+110x^71+255x^72+254x^73+431x^74+384x^75+480x^76+546x^77+668x^78+792x^79+761x^80+916x^81+921x^82+1044x^83+892x^84+1030x^85+806x^86+920x^87+835x^88+822x^89+673x^90+584x^91+546x^92+384x^93+313x^94+224x^95+195x^96+88x^97+92x^98+36x^99+66x^100+12x^101+41x^102+2x^103+16x^104+10x^106+8x^108+2x^109+1x^110+1x^112+1x^114+1x^116 The gray image is a linear code over GF(2) with n=168, k=14 and d=68. This code was found by Heurico 1.16 in 54.9 seconds.