The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 X^2+X 1 1 0 1 0 1 1 X^2+X 1 1 1 0 1 1 1 X^2 1 X^2+X 1 1 1 1 1 1 1 X^2+X 1 0 X 1 1 1 1 X 1 1 1 1 X^2+X X^2+X X^2+X 1 1 1 1 1 1 X X^2 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 X^2+1 1 X^2+X X+1 1 0 0 X+1 1 X^2+X X^2+1 1 1 0 1 X X^2+X+1 X^2+1 X^2 X^2+X X^2+1 0 1 X+1 1 1 X^2+1 X^2 X+1 X^2+X+1 1 X^2+X+1 X^2 X^2+X X^2+1 1 1 1 X+1 X^2 X X^2+1 X+1 X+1 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 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 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 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 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 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+93x^56+40x^57+216x^58+100x^59+502x^60+164x^61+474x^62+212x^63+550x^64+196x^65+522x^66+172x^67+383x^68+108x^69+190x^70+28x^71+108x^72+4x^73+6x^74+14x^76+5x^80+5x^84+3x^88 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 0.992 seconds.