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 0 X X 0 0 1 0 1 1 X 1 X 1 1 1 1 1 X 1 1 1 0 0 1 1 1 1 X^2 1 1 1 0 1 1 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X X^2 X^2 0 X X^2+X 0 0 X^2+X X^2+X X^2 X^2+X X X^2 X^2 X X 0 X^2+X X 0 X^2 0 X X^2 0 X^2 X 0 X X X X^2+X X^2+X X^2 X^2 X^2+X X X 0 X 0 X^2+X 0 0 X^2 X^2 0 X X 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X^2+X X 0 X X^2 X^2+X 0 X^2 X X^2 X X^2 0 X X^2+X 0 X^2+X X^2 X^2 X X X X^2 0 X^2+X X X X^2+X X^2+X X^2+X 0 0 0 0 X^2+X 0 X^2 X^2 0 0 0 X X X^2 X^2+X X^2+X X^2 X^2 X 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 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 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 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 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 55. Homogenous weight enumerator: w(x)=1x^0+40x^55+91x^56+110x^57+208x^58+140x^59+232x^60+292x^61+313x^62+468x^63+429x^64+444x^65+336x^66+274x^67+171x^68+142x^69+112x^70+74x^71+77x^72+28x^73+38x^74+26x^75+20x^76+6x^77+13x^78+2x^79+2x^80+2x^81+2x^82+1x^84+1x^86+1x^102 The gray image is a linear code over GF(2) with n=256, k=12 and d=110. This code was found by Heurico 1.16 in 4.44 seconds.