The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 X X 1 1 1 1 X 0 X 1 1 0 0 0 1 1 X 1 1 1 1 0 1 1 1 1 1 X X 1 1 X 1 0 1 1 0 0 X X 1 X 1 1 1 X 1 0 1 1 1 1 1 1 1 X 1 0 1 0 1 0 1 1 0 0 1 X+1 1 X 1 0 X 1 X+1 1 1 X 0 X+1 1 0 X 1 0 1 0 X+1 1 X X X+1 0 1 1 X 1 1 X+1 1 1 1 X X X 1 1 1 0 0 X 1 0 0 1 0 0 1 0 1 X 0 0 0 X 0 0 0 1 1 1 0 1 0 1 1 0 X 1 X+1 X+1 X X+1 0 1 0 1 0 X X+1 1 1 1 0 X+1 0 X 0 X+1 1 X+1 1 X+1 0 X 1 X 0 X+1 0 X+1 1 X 0 X+1 X 0 1 X+1 1 0 1 X+1 X+1 1 1 0 X+1 X+1 X X X+1 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 0 0 0 X X X 0 X X 0 X 0 X 0 X 0 0 X X X 0 0 X X 0 0 0 0 X 0 0 0 X X X 0 0 0 X X 0 0 0 0 0 X 0 0 0 0 0 X X X 0 X X 0 0 X 0 X X X X 0 0 0 X 0 0 X X X X 0 0 X 0 0 X X X X X X 0 X X X 0 0 X 0 0 0 0 0 X 0 X 0 0 X X 0 0 X X 0 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X X X 0 X X X X X X X X X X 0 X X X X 0 X 0 X X 0 0 X X X 0 0 X 0 X 0 0 X X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 X 0 X 0 0 X 0 0 X 0 X X X X X X X 0 0 X X 0 X X 0 X 0 X 0 0 X X 0 0 0 0 0 X X 0 0 0 X X 0 X X X 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 X X 0 X X 0 X 0 0 X 0 0 0 X X X 0 0 0 X 0 0 0 X X X X X X X X 0 X 0 0 0 X X 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 0 X X X 0 0 0 X X X X 0 X 0 0 X X X X X X 0 X X X X 0 X X X 0 0 X 0 X X 0 0 X X X X 0 0 0 0 X X 0 X X X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X 0 X 0 X X 0 0 0 0 X 0 X X X X 0 0 0 0 X 0 X 0 X 0 X X X 0 X 0 X 0 0 0 X X 0 X 0 X 0 0 X X X X X X X X X 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+59x^56+40x^57+153x^58+146x^59+221x^60+246x^61+329x^62+350x^63+385x^64+460x^65+469x^66+504x^67+500x^68+554x^69+442x^70+572x^71+440x^72+480x^73+357x^74+354x^75+298x^76+218x^77+202x^78+102x^79+94x^80+44x^81+75x^82+20x^83+36x^84+6x^85+18x^86+13x^88+2x^90+1x^92+1x^94 The gray image is a linear code over GF(2) with n=138, k=13 and d=56. This code was found by Heurico 1.16 in 11.2 seconds.