The generator matrix 1 0 0 0 0 1 1 1 0 1 1 0 0 X 1 1 1 X 1 1 1 0 1 1 0 0 1 1 1 1 1 X 0 0 1 X 1 X 1 X 0 1 0 1 X 1 0 0 1 X 1 1 1 0 0 1 1 X 1 1 1 X 1 0 1 0 1 1 1 X 1 1 1 1 1 1 1 0 X 0 X 0 1 0 0 0 0 0 0 0 1 1 1 1 1 X 1 1 1 X X X+1 1 1 X 1 X X 1 X 0 X+1 1 X 0 1 0 X 1 1 0 1 1 1 0 1 0 0 0 X+1 0 1 1 X+1 1 1 1 0 0 1 0 X 1 X+1 1 1 1 X X+1 X 1 X X+1 0 1 X 1 X 1 X X 0 0 0 1 0 0 0 1 1 1 1 X 1 0 X+1 X+1 X+1 X 0 X X 1 1 0 X X+1 1 1 X+1 1 X 0 X 1 1 1 1 0 1 X 1 1 X+1 X+1 1 X X X 0 X+1 1 1 X+1 X 1 X 0 1 1 0 0 X X+1 1 X X+1 1 X 0 0 0 1 0 1 X+1 1 X 1 1 0 X 1 0 0 0 1 0 1 1 0 1 0 X+1 X+1 1 X X+1 1 X X+1 X X+1 X X 0 1 1 1 X X 1 0 1 0 0 1 1 0 X 0 0 0 0 0 X+1 X X+1 1 1 1 X X+1 1 0 X+1 X+1 0 0 X 1 1 0 0 1 1 X 0 1 X X+1 X+1 X X 1 X X X+1 1 X 1 1 X 1 0 0 0 0 1 1 0 1 1 X 0 X 1 X+1 0 X+1 X+1 1 0 X+1 X X+1 X+1 1 0 1 X+1 X+1 X+1 X+1 1 X+1 1 X 0 0 X+1 X 0 1 X 0 1 X X 0 X+1 X X+1 X X 1 X X+1 X+1 0 1 X+1 X 0 0 1 X+1 0 0 X 1 X+1 X+1 X 0 0 0 X X+1 X X+1 0 1 1 0 0 0 0 0 0 X 0 0 0 X 0 X X 0 X X X 0 X 0 0 X 0 X 0 0 X X 0 0 0 X 0 X X X 0 0 0 0 0 X X 0 X 0 0 X 0 X X X 0 0 X X X 0 0 0 X X X 0 X 0 X 0 0 0 X 0 0 0 0 0 X X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X 0 X X 0 X X X X X X X 0 0 X X 0 X X X X 0 X 0 X 0 X 0 0 X X 0 X 0 0 X X 0 X X X 0 X X 0 0 X X X 0 0 0 0 X X 0 0 0 0 0 0 0 0 0 X 0 0 X X X 0 0 X X X X 0 X X X X 0 X X 0 0 X X X 0 0 X X X 0 0 X X 0 X X X X X 0 0 0 X X X 0 0 0 0 X 0 X X X 0 0 0 X X 0 0 X 0 X 0 X X X X 0 0 X X 0 0 0 0 0 0 0 0 X X X 0 X X X X X 0 0 X X X 0 X 0 0 X 0 X 0 0 0 0 0 X X X X X X 0 0 0 0 X 0 X X X 0 0 X 0 X 0 X X X X X X X X X X X X 0 0 0 X X X 0 X X 0 X 0 X 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+288x^68+606x^70+1026x^72+1264x^74+1487x^76+1666x^78+1845x^80+1836x^82+1856x^84+1458x^86+1268x^88+848x^90+540x^92+230x^94+109x^96+20x^98+20x^100+8x^102+6x^104+1x^108+1x^112 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 98 seconds.