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 X 1 0 1 1 1 1 X 1 X 1 1 0 1 1 1 0 1 0 X 1 X 0 1 1 X 1 1 X^2 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X 0 X^2+X X^2 0 X^2+X X X^2 X^2+X 0 X^2 X^2+X X X^2+X X X 0 X^2 0 X^2 0 X^2+X X^2+X X^2+X X X X X^2+X X 0 X^2+X X^2+X X^2+X X^2+X X X X X^2+X X^2+X X 0 X X^2+X X^2+X X^2+X X 0 0 X^2+X X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 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+87x^56+8x^57+119x^58+16x^59+172x^60+88x^61+272x^62+160x^63+290x^64+120x^65+232x^66+80x^67+159x^68+40x^69+110x^70+50x^72+29x^74+4x^76+2x^78+3x^80+4x^82+1x^84+1x^104 The gray image is a linear code over GF(2) with n=256, k=11 and d=112. This code was found by Heurico 1.16 in 0.491 seconds.