The generator matrix 1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 X 1 X 0 1 0 1 0 1 1 0 1 X 1 1 1 0 1 0 X X 0 0 1 X 1 1 1 X X 0 X X 1 0 1 1 X 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 X+1 X 1 1 X 0 0 1 1 X+1 1 0 X 1 X 1 1 X 1 X X X+1 0 0 1 X+1 0 1 1 1 X 1 0 1 X+1 X 1 X 1 1 X 1 1 X 1 1 1 1 X+1 X X X+1 1 1 0 0 1 1 1 0 1 0 1 X+1 0 X 0 X+1 1 X+1 1 1 X 0 X+1 1 X X+1 1 0 X+1 X+1 X+1 X+1 1 X 0 X X 0 1 1 X X+1 1 X+1 1 X 0 X+1 1 1 X+1 X 1 1 X X X+1 1 1 0 0 1 0 X+1 1 X 0 0 0 X 0 0 0 0 0 X X X X X 0 0 0 0 0 0 0 X 0 0 0 X X X X X 0 X 0 0 X X X 0 0 0 0 X X 0 0 X 0 X 0 X X 0 0 X 0 0 X X 0 0 X 0 X 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X X X X 0 X 0 X X 0 X 0 X 0 0 0 X X 0 X 0 X X X 0 X X 0 0 X X 0 X 0 0 X 0 X X X 0 X X 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X X 0 0 X X X 0 X X 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 X X 0 X 0 0 X X X 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X 0 0 0 X X X 0 X X X 0 X X 0 X 0 X 0 0 X X X 0 0 X X 0 0 0 0 X X X 0 0 X 0 X X 0 0 X 0 X 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 X X X X X 0 0 X 0 X 0 X X X X X X 0 0 0 0 0 X 0 0 0 X X 0 X 0 0 0 0 0 X 0 0 0 0 0 X X X X X 0 0 0 0 0 0 0 0 X X X X X X 0 X 0 0 0 0 0 X 0 0 X X X 0 X 0 0 0 X X 0 0 0 X 0 X X X 0 X 0 X 0 0 X 0 X X 0 0 0 X 0 0 0 X X X 0 X generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+157x^54+294x^56+387x^58+498x^60+491x^62+510x^64+518x^66+474x^68+334x^70+205x^72+115x^74+50x^76+39x^78+13x^80+4x^82+2x^84+3x^86+1x^88 The gray image is a linear code over GF(2) with n=128, k=12 and d=54. This code was found by Heurico 1.16 in 14.4 seconds.