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 0 X X 0 1 X X X 0 1 1 1 1 1 0 0 1 1 1 0 X 1 0 1 1 1 1 1 1 X X 1 X X 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 0 X 1 1 1 0 1 1 1 1 X X+1 X+1 X X+1 0 1 X X X 1 X 0 X+1 0 X+1 X+1 X+1 0 1 X 0 0 0 1 X X 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 1 0 X 0 X X 0 1 1 1 1 X X+1 X X+1 X+1 X+1 1 1 X 1 X 1 0 X 1 X+1 X+1 0 X 0 1 0 X X 1 X 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 X+1 1 0 X+1 1 X X 0 1 0 0 1 X X X X+1 0 0 0 X X 1 1 1 1 1 1 0 X X+1 0 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 1 X X X+1 0 X+1 X 0 0 X X+1 1 X+1 X 1 X X+1 X X X+1 X 1 1 1 X+1 0 X X X 1 0 0 0 X X+1 0 X+1 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 X 0 X 0 0 0 X 0 X X X X 0 X 0 0 0 0 X X 0 0 0 X X X X X X 0 X X 0 0 0 0 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 0 0 X 0 0 X X X X X X 0 0 0 0 X X X 0 0 0 0 0 0 X X 0 X X X 0 X 0 X X X 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 X X X X X X X X X X X X X 0 X X X X 0 X X X 0 X X X 0 0 X X X X 0 X 0 0 X generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+219x^58+516x^60+730x^62+764x^64+919x^66+1017x^68+957x^70+929x^72+764x^74+640x^76+386x^78+198x^80+105x^82+27x^84+15x^86+3x^88+1x^90+1x^96 The gray image is a linear code over GF(2) with n=138, k=13 and d=58. This code was found by Heurico 1.16 in 11.2 seconds.