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 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 X 1 X 1 X^2 1 X^2 1 0 X^3+X^2 0 X^2 0 0 X^2 X^2 X^3 X^3 X^2 X^3+X^2 0 X^3 X^2 X^2 0 X^3 X^3+X^2 X^2 0 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2 0 0 X^3+X^2 X^2 0 0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 0 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^3+X^2 0 0 0 X^3 X^2 0 X^3+X^2 0 0 X^2 X^2 X^3 X^2 0 X^3 X^2 X^2 0 0 X^3+X^2 X^2 0 X^3+X^2 X^3+X^2 0 X^3 X^2 X^2 0 X^3 X^2 X^3+X^2 0 0 X^2 0 X^2 X^2 X^3 X^2 0 X^2 X^3+X^2 0 X^2 0 X^3+X^2 0 X^3 0 X^3 0 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3 X^3+X^2 0 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 0 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 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 0 0 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 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 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 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 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 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+48x^66+123x^68+96x^69+137x^70+416x^71+447x^72+416x^73+119x^74+96x^75+82x^76+39x^78+11x^80+9x^82+6x^84+1x^88+1x^132 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 0.484 seconds.