The generator matrix 1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 0 X 1 1 X 1 X 1 1 1 1 0 X X 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 X 1 1 1 X 0 X 0 X 1 0 1 0 X 1 X 1 0 1 0 0 0 0 1 1 0 X X 1 0 1 X X 0 0 1 0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X 1 X 0 1 X 1 X 1 1 1 1 X 1 1 X 0 X X+1 0 X X+1 X+1 1 X+1 1 X+1 1 1 0 1 X+1 0 0 X X+1 1 1 1 X X 0 1 X X+1 X 1 0 1 0 1 0 X 1 1 X X X X 0 1 X X X 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 X+1 X 1 1 X+1 0 0 X 1 0 X+1 1 X+1 1 0 0 X+1 X+1 1 X X+1 X 0 0 X+1 X X X 1 X X 1 1 1 X+1 1 0 X X+1 0 1 1 X+1 1 0 0 X X X+1 0 X+1 X 1 X X+1 1 X+1 0 X 1 X+1 X 0 0 X+1 0 X+1 X+1 1 0 0 0 1 0 0 0 1 1 1 X+1 X+1 1 X 0 X+1 0 1 X X+1 X X+1 X+1 1 1 0 X 1 0 0 1 X X X+1 X X 1 X 0 X+1 0 X+1 X+1 1 X+1 X 1 X+1 0 0 X+1 X 1 0 0 X X 0 1 1 1 X X 1 X X 1 X+1 X X 0 1 0 1 X X 1 X 0 X+1 1 1 0 1 0 0 0 0 1 0 1 1 X X+1 1 1 1 0 X+1 0 1 0 1 0 X X X+1 0 X+1 X+1 X 1 X+1 1 0 0 X+1 X+1 X+1 X X 1 1 0 0 1 X 1 X+1 1 X+1 X+1 X+1 0 1 0 X+1 0 1 1 X 1 0 1 X 1 X 0 0 0 X X X+1 X+1 1 1 1 X+1 0 X X 1 1 X 1 1 X X+1 0 0 0 0 0 1 1 X X+1 1 0 X 1 X+1 0 X X X+1 1 X+1 0 X+1 0 0 1 1 0 1 X X+1 0 X+1 0 X 1 1 X 0 X+1 1 1 X 1 0 1 1 1 X+1 0 X 0 X 1 X 1 1 0 X+1 0 1 1 X X+1 1 X+1 1 0 X 1 0 0 1 X+1 X 1 X+1 1 X 0 1 X+1 0 X 1 0 0 0 0 0 0 X 0 X 0 0 0 0 0 X X X 0 0 X X 0 X 0 X 0 0 0 X X X 0 0 0 0 X X 0 0 0 X X 0 X X 0 0 X 0 0 X X X 0 X X X 0 X 0 0 X 0 X X 0 X X X 0 0 X X X X 0 0 X X X 0 X X X generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+148x^72+432x^74+719x^76+778x^78+907x^80+760x^82+908x^84+846x^86+722x^88+698x^90+542x^92+352x^94+212x^96+86x^98+54x^100+16x^102+10x^104+1x^108 The gray image is a linear code over GF(2) with n=168, k=13 and d=72. This code was found by Heurico 1.16 in 13.5 seconds.