The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 X 1 1 1 1 1 0 X^2+X 1 1 1 1 X 1 X^2 1 X X^2+X 1 1 1 1 1 1 1 1 1 X 1 X^2+X 1 X 1 1 1 1 X 1 1 X 1 1 1 1 X^2 0 1 X 0 0 X X^2 X 0 1 0 1 1 0 X^2+X+1 1 X X+1 1 1 X^2+X+1 X^2 X^2+X 1 X 1 1 0 X+1 X 1 1 X^2+1 1 X+1 1 1 0 X^2 X^2+1 X^2 X+1 X^2 X^2+X+1 X^2 X^2+1 1 X 1 X 1 X^2 X^2+X 0 X^2+X 1 X^2+X 1 1 X^2+1 X^2 0 X^2+1 1 1 X^2 1 X X^2 X 0 X^2 1 X+1 0 0 X 0 X^2+X 0 0 0 X^2 X^2 X^2 X X^2+X X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 X^2+X X^2 X X^2+X X^2+X 0 X^2 X 0 X^2 X X^2+X X^2+X X X^2 X X^2 X X X^2+X 0 X^2+X X 0 X 0 0 0 X^2+X X^2+X 0 0 X^2+X X^2+X X^2+X X 0 X X X 0 X 0 0 0 0 X 0 0 X X^2 X^2+X X X 0 X^2+X X X^2 X X X X^2+X 0 X^2 0 X 0 X^2 X^2+X X X^2 0 X^2 X^2+X X X^2+X X^2 0 0 0 X X X^2 0 X^2 0 X X X^2+X X^2 X^2+X X^2+X X X 0 X^2 X^2 X^2 X X^2+X X^2+X 0 X^2+X X X^2+X X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 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+211x^56+120x^57+436x^58+336x^59+697x^60+496x^61+800x^62+600x^63+965x^64+600x^65+852x^66+480x^67+511x^68+288x^69+320x^70+120x^71+187x^72+32x^73+80x^74+39x^76+8x^78+12x^80+1x^84 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 93.3 seconds.