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 1 0 1 0 0 0 X 1 1 1 0 1 1 0 0 0 X X X 0 1 X 1 X 1 0 1 X X 0 1 1 X 1 1 1 1 0 X X 1 1 1 X 1 X X 1 X 0 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 1 X 1 1 0 1 1 X X+1 0 0 1 X+1 1 1 X 1 1 0 X 1 0 X X+1 X 1 1 X 1 0 0 1 0 1 1 1 1 0 X 0 1 X+1 X+1 X+1 X 0 X 1 1 0 1 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 0 X 0 X 0 X X X X 1 1 X+1 X+1 1 1 1 1 1 1 X+1 1 1 1 1 1 1 X+1 X+1 1 1 X+1 1 1 0 X+1 1 X 1 1 X+1 0 0 1 0 X+1 1 X X+1 X X 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+1 1 0 0 0 1 0 1 X 0 0 0 X X 1 X+1 X+1 X+1 X+1 1 0 0 X 0 1 1 X+1 X+1 X+1 X+1 1 1 X+1 X X+1 X+1 1 X 0 X X+1 X+1 0 X+1 0 X 1 X 0 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 X+1 0 1 X X 1 1 X+1 X 1 X X 1 0 1 X+1 1 X 0 X X+1 X+1 1 X X+1 X+1 X X+1 0 X 1 1 0 1 0 X+1 1 X 0 0 0 1 0 X+1 1 1 X 0 X 1 1 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 1 X+1 0 X+1 1 0 X+1 X+1 0 X+1 X+1 X 0 X+1 X+1 0 X 0 X+1 0 1 X X+1 X+1 0 1 1 X+1 0 X 1 1 X X 0 0 X+1 X 1 1 X 1 0 X+1 1 X+1 0 X X+1 1 X+1 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 X X X+1 X X+1 0 X X+1 1 0 1 1 1 1 X+1 X+1 0 X X+1 X X+1 X X 0 X 1 1 X+1 X X+1 1 X X+1 X 1 0 X+1 X+1 1 1 0 X+1 X+1 X X+1 1 1 0 1 X generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+247x^68+630x^70+1065x^72+1246x^74+1529x^76+1668x^78+1817x^80+1856x^82+1673x^84+1602x^86+1249x^88+882x^90+491x^92+276x^94+106x^96+32x^98+12x^100+1x^104+1x^136 The gray image is a linear code over GF(2) with n=162, k=14 and d=68. This code was found by Heurico 1.16 in 96.7 seconds.