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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 0 1 X^2 1 X 0 X X^3+X^2 X^2+X 0 X^2+X X^3+X^2 X^3+X X^2+X 0 X^3+X X^3+X^2 X^3 X^3+X X^2 X^2+X X^3+X^2+X 0 X^3+X^2 X^3+X 0 X^2+X X^3+X^2 X^3+X 0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X 0 X^2+X X^3+X^2 X^3+X X^2 X^3+X^2+X 0 X X^3 X^2+X X^2 X^3+X X^3 X^3+X^2+X X^3+X^2 X 0 X^3 X^2+X X^3+X^2+X 0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^3+X^2 X^2 X^2 X^3+X X^3+X X X 0 0 X^3 X^3 X^2+X X^2+X X^3+X^2+X X^3+X^2+X 0 X^3 X^3 X^3+X^2 X^3 X X^2+X X^3+X^2 X^2+X X^2 0 0 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 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 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 0 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 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 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 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 0 0 0 X^3 0 X^3 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 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 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 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 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 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 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 0 X^3 generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+66x^77+105x^78+86x^79+226x^80+238x^81+623x^82+220x^83+215x^84+104x^85+103x^86+46x^87+5x^88+6x^89+1x^90+2x^93+1x^156 The gray image is a linear code over GF(2) with n=656, k=11 and d=308. This code was found by Heurico 1.16 in 1.13 seconds.