The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 X 1 1 1 0 1 1 0 1 1 X X 1 1 1 1 X^2+X 1 1 1 X 1 1 1 1 1 X^2 1 0 1 X^2+X 1 X^2+X 1 1 0 1 0 0 X X^2 1 X 0 1 1 X^2 1 1 1 0 X X 1 0 1 1 X^2+X X^2+X+1 1 0 X+1 1 X 1 X^2+1 1 0 1 X X^2+X+1 1 X^2 1 1 1 X X^2+X+1 X^2+1 X 1 X+1 X^2+X+1 0 1 X^2 1 X^2+1 X^2+X X^2 1 1 1 X^2+1 1 X^2 1 1 1 1 X^2+X+1 1 1 0 X X^2+1 1 1 1 X^2+X+1 1 X X^2 0 1 X^2+X X 0 0 0 X 0 X^2+X 0 X^2+X X^2 X X X^2+X 0 X 0 X^2 X^2+X X^2 X^2+X X^2+X X^2 X^2+X 0 X^2 X^2+X X^2 X 0 X^2 X 0 X^2+X X X X 0 X X X^2+X 0 X^2 X^2 X^2 X X 0 X^2+X X X^2 0 X^2+X X X X 0 0 X^2+X 0 X^2+X X^2 X X X X^2+X 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 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 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 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 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 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+22x^56+132x^57+159x^58+246x^59+298x^60+334x^61+386x^62+358x^63+387x^64+330x^65+359x^66+292x^67+266x^68+192x^69+93x^70+112x^71+34x^72+24x^73+17x^74+14x^75+10x^76+10x^77+8x^78+2x^79+4x^80+2x^81+1x^82+2x^84+1x^86 The gray image is a linear code over GF(2) with n=256, k=12 and d=112. This code was found by Heurico 1.16 in 0.965 seconds.