The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X 0 1 1 1 1 0 1 X 1 X 1 0 X X 1 1 X 0 1 1 1 1 X 1 0 1 0 1 1 0 0 1 1 0 0 0 1 X 1 0 0 0 1 0 X 1 1 X 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 X+1 X+1 1 X 1 X X+1 0 1 1 0 1 X X 0 1 1 X X+1 1 0 1 X 0 X 1 1 X+1 0 1 1 1 0 X 1 1 1 X 1 1 X 1 0 0 1 1 X+1 X 0 X+1 X+1 1 0 X 1 1 0 1 X 0 0 1 0 1 1 0 1 0 1 1 0 0 1 X+1 X+1 X 0 1 X+1 X+1 X 0 1 0 X X 0 0 1 1 X 1 1 1 X 1 1 1 X X 1 X 0 0 1 0 1 0 X 0 0 0 1 X+1 1 X 1 1 0 X 0 1 X+1 1 1 X+1 X X 0 0 0 1 1 0 1 1 1 0 1 X 1 1 0 X 1 X+1 X X+1 1 1 0 0 X+1 X 0 1 1 0 0 X 0 X+1 X+1 0 0 1 X+1 X 1 X+1 0 1 1 X+1 1 X+1 X X+1 1 X X+1 X 1 0 X+1 0 X+1 0 1 X+1 X X X X 0 0 1 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X 0 X 0 X X 0 X 0 0 X 0 X 0 X 0 X 0 X X 0 0 X X 0 0 0 X X X X X 0 0 X X X 0 X X 0 0 X X X 0 X 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X X 0 X X X 0 X 0 X X X X X 0 X X X X 0 X 0 X 0 X 0 0 X 0 0 X X X X X 0 X 0 0 X X X 0 X X 0 X 0 0 0 0 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 0 0 0 0 0 X X X X X X X X X X X X X X X X 0 X X X X X X X X 0 X 0 X 0 0 X 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 X 0 0 X X 0 X 0 0 X 0 X X 0 X X X X 0 X 0 0 X 0 X 0 X X 0 0 X 0 0 0 0 X X X 0 X X 0 X 0 X 0 0 0 0 X X 0 X X X 0 0 0 0 0 0 0 0 X 0 X 0 0 0 0 X 0 0 0 0 X X X X 0 X 0 X X X 0 0 0 X 0 X 0 0 X X 0 0 X 0 0 X 0 X 0 X 0 X X 0 0 0 X 0 X X X X X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X 0 0 X 0 0 X 0 X X X X 0 X X X 0 0 X X 0 X X X 0 0 X X X 0 X X 0 X X X X 0 0 X X 0 0 X X X X X X X 0 X X 0 X generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+195x^56+438x^58+892x^60+1256x^62+1511x^64+1846x^66+2005x^68+2064x^70+1871x^72+1730x^74+1224x^76+696x^78+376x^80+146x^82+98x^84+16x^86+13x^88+4x^92+1x^100+1x^104 The gray image is a linear code over GF(2) with n=138, k=14 and d=56. This code was found by Heurico 1.16 in 81.8 seconds.