The generator matrix 1 0 0 1 1 1 X 1 1 X^2+X 1 1 X X^2+X X 0 1 1 1 1 X^2+X X^2+X 1 X^2 0 1 1 1 X^2+X 1 1 0 X^2+X 1 1 X^2 1 X^2+X X^2 1 1 X^2 0 X X 1 X^2 1 1 1 0 1 X^2 X X^2 1 X 0 X X^2+X 1 X^2 X^2 1 0 1 0 X 1 X^2+X+1 1 X^2+X 0 X^2 1 X+1 X^2+X 1 1 1 X^2+X X^2+X+1 0 X^2+1 1 1 X 1 X^2+X 1 X^2+X 1 1 X^2 X+1 1 X^2+X 0 X^2+1 1 1 X 1 X^2 X^2+X+1 1 1 1 1 X+1 1 X^2+1 X^2+X 0 X X+1 1 0 1 0 1 1 0 1 X^2+1 X^2 X X^2+1 0 0 1 1 X^2+X+1 X^2+X 1 X+1 X^2+X 1 1 0 1 X+1 X X+1 X^2 1 X^2+X+1 X^2+X 0 X X X^2+1 1 0 X^2+1 X+1 X+1 X+1 1 X^2 1 X X^2 X^2+X 1 1 0 X+1 X X^2+1 X+1 X+1 X^2+1 X^2+X X^2 X^2+X+1 X^2+X 0 1 X^2+X+1 X+1 1 X^2+X 1 X 1 1 X X+1 1 1 X+1 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 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 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 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 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+47x^56+234x^57+151x^58+788x^59+352x^60+1026x^61+338x^62+1156x^63+312x^64+1096x^65+374x^66+882x^67+247x^68+542x^69+129x^70+274x^71+60x^72+100x^73+20x^74+34x^75+5x^76+8x^77+9x^78+2x^79+2x^81+3x^82 The gray image is a linear code over GF(2) with n=256, k=13 and d=112. This code was found by Heurico 1.16 in 3.33 seconds.