The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X X 1 0 X 0 1 0 1 1 1 X 0 0 1 1 1 1 1 1 1 1 X X 1 X 1 1 1 0 X 1 1 0 X 1 X 0 X 1 X 1 X X X X 1 X X 1 1 1 0 X 1 0 1 0 0 0 1 1 1 0 X X+1 X+1 1 1 X 0 0 0 1 X 1 X+1 1 1 0 0 1 0 X X+1 X X+1 X+1 0 X 1 X X+1 1 X+1 X+1 0 0 1 X 0 1 0 0 1 1 1 X+1 0 X 0 0 X 1 X 0 X 0 X+1 X 1 1 0 0 0 1 0 1 1 0 1 0 1 1 X 0 1 1 X 1 X X 1 1 X+1 0 1 1 1 0 0 1 X 0 X+1 X 1 X X 0 0 X+1 X+1 X+1 X+1 0 0 1 X 0 X X X X X 0 1 X+1 1 1 1 X+1 1 0 0 X 0 1 X 1 0 0 0 0 1 1 0 1 1 1 0 X+1 X 1 X 1 X+1 0 1 0 X+1 0 0 1 X+1 0 X 1 X 0 X X+1 X 0 X X 1 1 X 1 X+1 1 X 1 0 0 X X+1 1 X+1 X+1 0 1 X X 1 1 X+1 X+1 X X+1 1 1 X+1 X+1 X+1 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 X X X X X 0 X 0 0 X X 0 0 0 0 X X X 0 0 0 0 0 X X X X 0 X 0 X X X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X X X X X 0 0 0 X 0 0 X X 0 X X X 0 0 X X 0 X 0 X 0 X 0 X X X 0 0 X 0 0 0 X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X X 0 0 X 0 X X 0 0 0 X 0 X X X X 0 0 0 0 X X X X X X 0 X 0 0 X X X X 0 0 0 0 X X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X X 0 0 X X X X 0 0 X X 0 X X 0 0 0 0 X X X 0 X 0 0 0 0 0 0 X X X 0 0 X X 0 0 0 X X X X X 0 0 0 0 X 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 0 0 X 0 0 X 0 0 X 0 X X X 0 X X 0 X 0 X X 0 0 0 X X 0 X 0 0 0 0 0 X 0 X 0 X 0 X 0 X 0 0 X X X X X X 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+54x^56+98x^57+193x^58+234x^59+283x^60+334x^61+380x^62+428x^63+444x^64+502x^65+473x^66+478x^67+517x^68+444x^69+459x^70+510x^71+421x^72+426x^73+347x^74+306x^75+247x^76+210x^77+154x^78+84x^79+60x^80+30x^81+35x^82+6x^83+15x^84+4x^85+7x^86+2x^87+3x^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 10.6 seconds.