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 1 1 1 1 1 1 X 1 1 X^2 1 1 1 1 1 1 1 1 1 1 1 1 X X X 0 X^3+X^2 0 X^2 0 0 X^2 X^3+X^2 0 0 X^2 X^3+X^2 0 X^2 X^3+X^2 0 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 0 X^3+X^2 X^3 0 X^3+X^2 X^3+X^2 X^3 X^2 X^2 0 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3+X^2 X^2 0 X^2 X^3 X^3+X^2 0 0 0 X^3+X^2 X^3 X^2 X^3 X^3 X^2 0 X^3+X^2 0 X^3+X^2 X^2 X^3 X^2 X^2 X^3 0 0 X^3 0 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^2 0 X^3+X^2 0 0 X^3+X^2 X^2 0 X^3+X^2 X^2 0 X^3+X^2 0 X^2 0 0 X^2 0 X^3+X^2 X^2 X^3 0 X^3+X^2 X^2 X^3 0 X^2 X^2 0 X^2 X^3 X^3 X^3+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 0 X^3 X^3+X^2 X^3+X^2 X^2 X^2 0 X^3 0 X^3 X^3 X^3+X^2 0 X^3 X^2 0 0 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 0 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 0 X^3 0 0 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 X^3 X^3 X^3 0 X^3 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 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+146x^72+64x^74+342x^76+1024x^77+256x^78+138x^80+58x^84+18x^88+1x^144 The gray image is a linear code over GF(2) with n=616, k=11 and d=288. This code was found by Heurico 1.16 in 3.05 seconds.