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 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 X^3 1 1 1 X 1 1 X^2 X 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 X^3+X^2 0 0 X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 0 X^3+X^2 0 X^2 0 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3 0 0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2 0 0 0 X^2 X^2 X^3 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 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 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 0 0 X^3 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 0 0 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+132x^64+92x^66+906x^68+768x^70+28x^72+24x^74+52x^76+30x^80+12x^82+2x^84+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 0.437 seconds.