The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 X X 1 1 1 1 X X 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 X 1 1 1 1 1 X 1 X 0 0 1 0 0 X 1 1 1 X 0 X 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 X+1 1 X 1 0 X X+1 1 1 1 X 1 1 1 0 X 0 1 1 1 1 0 0 X+1 X 1 X X 1 X+1 1 1 1 X+1 1 X+1 X+1 X 1 X 1 1 1 X 1 0 1 X 1 X 1 1 1 X 0 X+1 0 1 0 0 1 1 1 0 1 0 1 1 0 X 1 X+1 X+1 X 0 X+1 X X+1 1 X+1 1 0 X+1 X 1 0 X+1 0 1 0 0 1 1 1 1 X+1 1 X X 1 0 X 1 0 1 X+1 1 0 X+1 X X X+1 1 1 0 X 1 0 1 X X X+1 X 0 1 1 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X 0 X 0 X X 0 X X 0 X 0 0 0 X 0 X X 0 0 0 0 X X X X X X X 0 0 0 0 X X 0 0 0 X 0 X X X 0 X X X X X 0 X 0 0 0 0 X 0 0 0 0 0 X X X 0 X X 0 0 0 X 0 0 X X X 0 X 0 X 0 0 X X X 0 X X 0 0 X X 0 X X 0 X 0 0 0 0 0 0 X 0 0 0 0 X 0 X X X 0 X 0 X X 0 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X 0 X X X X X X X X 0 X X 0 X 0 X X X 0 X 0 X X X X X 0 0 0 X 0 X X X 0 X 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X X X X 0 X X 0 0 0 0 0 X 0 X X X X 0 0 X 0 X 0 X X X 0 X X 0 0 0 0 X X X X X 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X 0 X X X 0 X X 0 0 X 0 X 0 X X X X 0 0 X X 0 0 X X X X 0 0 X X 0 0 0 X X 0 X 0 0 X 0 0 0 0 X X 0 0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 0 0 X 0 0 X X 0 0 X 0 X X X 0 0 0 X 0 X X X X 0 X X 0 0 0 X X X 0 0 0 X X X 0 X 0 X 0 X X 0 X X X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X 0 0 X 0 X X 0 X X 0 X X 0 0 X 0 0 X X X X X 0 0 0 0 0 0 X X 0 0 X 0 X 0 X X 0 X 0 0 X X X 0 X 0 X 0 0 generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+167x^56+238x^58+651x^60+656x^62+960x^64+870x^66+1081x^68+968x^70+1022x^72+626x^74+495x^76+200x^78+174x^80+26x^82+43x^84+11x^88+2x^92+1x^96 The gray image is a linear code over GF(2) with n=136, k=13 and d=56. This code was found by Heurico 1.16 in 11.3 seconds.