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 1 1 1 1 1 X 1 1 X 1 1 1 1 1 1 1 X 1 1 X X X X 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 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 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 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 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 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 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 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 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 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 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 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 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 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 generates a code of length 63 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+50x^56+80x^58+48x^60+76x^62+512x^63+107x^64+76x^66+16x^68+4x^70+30x^72+20x^74+3x^80+1x^112 The gray image is a linear code over GF(2) with n=252, k=10 and d=112. This code was found by Heurico 1.16 in 0.208 seconds.