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 1 X 1 1 1 0 1 0 1 X 1 X 1 0 1 1 X 1 0 1 X X X 1 1 0 0 1 X 0 1 1 X 1 X 1 X 0 0 X 1 0 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 0 1 X+1 0 X 1 X+1 1 0 1 0 X 0 0 X+1 1 X X+1 1 0 X 1 X X+1 1 1 0 X 1 0 X X+1 1 0 1 1 0 0 1 1 X 1 0 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 0 X+1 X 0 X+1 0 X 1 1 0 X+1 X+1 X 1 X+1 1 1 X+1 1 X+1 X X+1 1 1 1 X X 1 X+1 1 X 1 0 X 0 X+1 X 1 0 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 1 0 0 X 1 X+1 1 0 X+1 0 1 0 X+1 1 X X+1 1 0 X X+1 X+1 X 1 1 0 X+1 X+1 0 1 1 X 1 0 X+1 0 1 X 0 0 X 0 X+1 0 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 X+1 1 1 X+1 X 1 X+1 1 X+1 X+1 X X+1 X+1 1 X 0 0 X X+1 0 0 X X 1 0 X+1 1 X+1 0 1 0 X+1 X X 1 0 1 1 X+1 1 X X+1 0 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 X 0 X X 0 0 X X X X 0 X 0 X X X X 0 0 0 X X 0 0 X 0 0 0 0 0 0 0 0 X X 0 0 0 X 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 X 0 0 X 0 0 X X 0 X 0 0 0 0 X X X 0 X X X X 0 X X 0 0 0 0 X X X 0 X X 0 0 X X 0 0 X 0 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 X X X X X X X X X X X X X X X X X 0 0 0 X X X X 0 X 0 X X X X 0 0 X X X 0 X X 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+85x^56+76x^57+198x^58+238x^59+296x^60+358x^61+394x^62+432x^63+404x^64+490x^65+450x^66+468x^67+439x^68+502x^69+459x^70+512x^71+489x^72+372x^73+350x^74+302x^75+240x^76+206x^77+150x^78+80x^79+77x^80+38x^81+36x^82+16x^83+17x^84+6x^85+5x^86+6x^90 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 10.5 seconds.