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 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 X 1 1 X^2 1 1 1 X 1 1 X 1 1 1 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 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 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 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 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 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 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 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+37x^56+31x^58+31x^60+32x^61+33x^62+352x^63+23x^64+352x^65+19x^66+32x^67+20x^68+17x^70+11x^72+19x^74+5x^76+5x^78+3x^82+1x^118 The gray image is a linear code over GF(2) with n=256, k=10 and d=112. This code was found by Heurico 1.16 in 0.214 seconds.