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 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 0 0 X^3 0 0 X^3 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 0 0 X^3 0 0 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 0 0 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+27x^56+58x^58+30x^60+256x^63+1305x^64+256x^65+44x^66+18x^68+11x^72+26x^74+15x^76+1x^124 The gray image is a linear code over GF(2) with n=512, k=11 and d=224. This code was found by Heurico 1.16 in 0.281 seconds.