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 X X^2 X^2 X 1 X 1 1 1 0 X 1 X^2 X 1 1 X 1 1 1 1 1 X^2 1 X 1 X 1 1 1 0 X 1 X^2 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 0 X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2 0 0 X^2+X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X X^2 X^2 X X^2+X X^2+X X^2+X X X^2+X X^2 X 0 X X^2+X X X X^2+X 0 X X^2 0 X X^2+X X^2 X X X^2 0 X X^2 X 0 X^2 0 0 X 0 X X X^2+X 0 0 0 X^2+X X^2+X X X X^2 0 X X^2 0 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X X^2 X X X^2+X X^2 X^2+X X X^2+X X X^2 X X^2 X^2 X^2+X X X^2 X^2+X X^2+X 0 0 0 0 X 0 X^2 X^2 X^2 X X^2+X 0 0 0 X X 0 0 X^2+X X^2+X X 0 0 0 0 X X 0 X^2+X X X^2 X^2+X X X^2 X^2 X X X^2 0 X^2+X 0 X X^2 X X X^2+X X^2 X^2 0 X^2 X X X^2+X X X^2 0 X^2 0 X^2 X^2+X X^2 X^2+X X^2 X^2 0 X^2+X X X^2+X X X^2+X 0 X X^2+X X^2+X X X 0 0 X^2 X 0 0 X^2 X 0 X X 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+51x^56+80x^57+109x^58+118x^59+322x^60+154x^61+458x^62+116x^63+626x^64+142x^65+671x^66+114x^67+403x^68+108x^69+217x^70+74x^71+93x^72+72x^73+62x^74+24x^75+39x^76+18x^77+17x^78+2x^79+2x^81+1x^82+1x^88+1x^98 The gray image is a linear code over GF(2) with n=260, k=12 and d=112. This code was found by Heurico 1.16 in 1.32 seconds.