The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X^2 X X^2 X X X 0 1 X 1 1 X 1 1 X X 1 1 1 X 1 X X X 0 1 X 0 0 X 0 0 0 0 0 0 0 X^2+X X X X X X^2 X^2 0 X X^2 X^2+X X 0 X^2 X^2 X 0 X X^2+X X^2 X^2+X 0 X X^2+X X^2+X X^2 X^2 X X^2 X X X^2+X X^2 X^2+X X X 0 0 X^2 0 X^2+X X 0 0 X^2 X^2 X X^2+X 0 0 X^2 X^2+X 0 0 X X^2 0 0 X 0 0 0 X X^2+X X X^2 X X^2+X 0 0 X X^2+X X^2+X X^2+X 0 X^2 X X^2+X X^2+X X^2+X X X^2 X^2+X X X^2+X 0 0 X^2 X X^2+X 0 X^2 X^2+X X X^2 0 X^2 X 0 0 X X^2 0 0 X X^2 X^2+X X X X^2 X X X^2+X X^2 X^2+X X X^2+X X 0 0 X^2 0 0 0 X 0 X X X 0 X^2+X X^2 X X^2+X 0 X X^2+X 0 0 X^2+X X X^2 X X^2 0 X^2 0 X X 0 X 0 0 X^2 X^2+X X^2 X^2+X X^2+X 0 0 X^2 0 X^2 0 X^2 X X X^2 X^2+X X^2 X^2+X X^2+X 0 X^2+X X^2 0 0 X^2+X 0 X X^2+X X X^2 X^2 0 0 0 0 0 0 X X 0 X X^2+X X 0 X X^2 X^2+X X^2+X 0 X X^2+X X^2 X^2 0 X^2+X 0 X 0 X X^2+X 0 X^2 X^2+X X^2 X^2 X X^2+X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X^2 X^2 0 X X^2+X 0 0 X^2+X X^2 X^2+X 0 0 X^2 0 X^2 X^2 0 X 0 X 0 X X 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 55. Homogenous weight enumerator: w(x)=1x^0+74x^55+122x^56+176x^57+256x^58+316x^59+377x^60+520x^61+533x^62+674x^63+735x^64+696x^65+844x^66+646x^67+568x^68+418x^69+298x^70+246x^71+182x^72+198x^73+100x^74+84x^75+54x^76+38x^77+17x^78+6x^79+8x^80+2x^81+2x^83+1x^92 The gray image is a linear code over GF(2) with n=260, k=13 and d=110. This code was found by Heurico 1.16 in 5.64 seconds.