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 X 1 X 1 1 1 1 1 1 1 1 X 1 X 1 X 1 X 1 X 1 1 1 X X 1 1 1 1 X X 0 X^2 0 0 0 0 0 0 0 0 0 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 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 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 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 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 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 generates a code of length 63 over Z2[X]/(X^3) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+68x^54+124x^56+46x^58+84x^60+224x^62+1024x^63+187x^64+80x^66+44x^68+72x^70+59x^72+2x^74+20x^78+12x^80+1x^104 The gray image is a linear code over GF(2) with n=252, k=11 and d=108. This code was found by Heurico 1.16 in 43.1 seconds.