The generator matrix 1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 X 1 1 X X 1 1 1 1 1 0 1 0 1 X X 0 0 1 1 X 1 X 1 1 0 1 0 0 0 0 X X X 1 1 0 1 X 1 X 1 X 1 X 1 X 0 1 1 X 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 1 0 X+1 0 X 1 X+1 X 0 X 1 X+1 1 X 1 X 0 1 X+1 1 1 X X 0 X+1 1 X+1 0 1 0 1 1 1 1 X X 0 1 0 1 0 0 X X+1 1 X 1 1 0 X X X+1 X+1 0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 0 1 1 1 X+1 0 1 0 X 0 1 1 X X 1 X 0 0 X+1 1 1 X 1 X 1 1 X 1 X 0 X+1 0 0 X 1 X X X+1 1 X+1 X X 1 X+1 X+1 1 X X+1 0 0 1 0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 0 1 0 1 0 0 1 0 0 X+1 1 1 X X+1 1 1 X+1 X 1 1 X+1 X X X+1 0 1 X+1 1 X+1 X X X X X X 1 1 1 X 1 X+1 0 1 0 X 1 X+1 1 1 X 1 0 1 0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 1 X+1 1 X 1 1 X X+1 1 X X 1 X X 1 1 0 X+1 0 X+1 X+1 1 X 1 X 0 0 X+1 X 1 1 X 1 X+1 1 X+1 X+1 X+1 1 X 0 X X X X+1 X+1 X+1 0 X X+1 X X 0 0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X X 0 X X 0 0 X 0 X 0 0 X X X 0 0 X 0 X 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X 0 0 X X 0 X 0 X 0 X X 0 X X 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X 0 X 0 X X 0 0 X X 0 0 X X X 0 X X 0 X 0 0 X 0 0 0 0 X 0 0 X X X X 0 0 X X X X X 0 0 0 0 0 X 0 0 X X X 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 0 0 X X X X X X X X X X X X X X X X X 0 X 0 X 0 X X X 0 X 0 X 0 X 0 X X X X 0 X 0 X 0 X X 0 0 generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+144x^66+446x^68+612x^70+737x^72+864x^74+889x^76+915x^78+935x^80+810x^82+672x^84+538x^86+323x^88+164x^90+81x^92+39x^94+12x^96+10x^98 The gray image is a linear code over GF(2) with n=156, k=13 and d=66. This code was found by Heurico 1.16 in 12.4 seconds.