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 0 1 1 1 X 1 1 0 1 1 0 1 X 1 1 X^2 1 1 1 X 1 X 0 X 1 X^2 X^2 0 0 0 1 X 1 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X 0 X^2 X X^2+X X^2 0 X^2 X X^2 X 0 X^2 X X^2+X 0 X^2 X^2+X X X^2 X^2+X X 0 X^2+X 0 X X^2+X X 0 0 0 X^2+X X^2 X X X^2+X 0 X X^2+X X^2+X X X^2 0 X 0 X X X^2 X^2+X 0 X^2 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X^2+X X X X^2 X^2 X^2 X 0 X^2 X^2+X 0 X^2+X 0 0 X^2+X X 0 X^2 0 0 X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2+X X 0 X^2+X X^2+X X X^2+X X X^2 X X^2+X 0 0 X^2 X^2+X 0 X^2+X X X^2 X^2+X X X^2+X X^2+X X 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 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+60x^56+74x^57+115x^58+226x^59+127x^60+370x^61+118x^62+548x^63+127x^64+704x^65+105x^66+546x^67+98x^68+302x^69+96x^70+174x^71+72x^72+76x^73+57x^74+36x^75+23x^76+8x^77+15x^78+6x^79+4x^80+2x^81+3x^82+2x^86+1x^94 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 1.45 seconds.