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 1 X^2 1 1 1 1 1 1 1 1 X 1 1 1 1 1 X 1 1 X 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^2 X^3 X^3+X^2 X^3+X^2 0 X^3+X^2 0 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 X^3+X^2 0 X^3 X^2 X^2 X^3 0 X^3+X^2 X^3+X^2 X^2 0 X^3 X^3+X^2 X^3 0 X^2 0 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^3 0 0 X^3+X^2 X^3+X^2 0 X^3 X^3+X^2 X^2 0 X^2 X^2 0 X^3 X^3+X^2 0 X^3+X^2 X^3+X^2 X^3+X^2 0 0 0 X^3 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 X^3 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 0 0 0 X^3 0 0 0 X^3 0 0 0 0 X^3 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 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 0 0 0 0 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+43x^66+104x^68+238x^70+1233x^72+256x^73+52x^74+40x^76+34x^78+21x^80+17x^82+8x^84+1x^136 The gray image is a linear code over GF(2) with n=576, k=11 and d=264. This code was found by Heurico 1.16 in 7.41 seconds.