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 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 X 1 1 X 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 0 0 X^3 0 0 X^3 0 0 0 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 0 0 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+150x^64+448x^68+1024x^69+256x^70+112x^72+56x^80+1x^128 The gray image is a linear code over GF(2) with n=552, k=11 and d=256. This code was found by Heurico 1.16 in 89.9 seconds.