The generator matrix 1 0 1 1 1 X^3+X^2+X X 1 1 X^3 1 1 X^2 1 1 1 X^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 1 1 X^3+X 1 0 1 1 X^3+X^2 1 X^3+X^2+X 1 X^2+X 1 X 1 X^3 1 1 0 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X^3 1 1 1 0 1 1 1 X^3 1 1 1 X 1 1 1 1 X^3+X 1 0 1 X+1 X^2+X X^3+X^2+1 1 1 X^3+X^2 X^2+X+1 1 X^3+X 1 1 X^3 X+1 X^3+X^2+X 1 X^3+X^2+X+1 X^2 1 X 1 X+1 X^3+X^2+X+1 X^2+1 X^3+1 0 1 X^2+1 1 X^3+X^2+X X^3+X+1 1 X^3+1 1 X^3 1 X^3+X^2+1 1 X^3+X^2+X+1 1 X X^2+1 1 X^3+X X^2 X^2 X^3+X^2+X X^3+X X^3+X 0 X^3+X^2+X X X^2 X^3+X^2+X X^2+X X^3+X X X^3+X X^3+X^2 0 X^3+X+1 X^3+X^2 1 0 X^2 X^2 1 0 X^2+X+1 1 1 X^3 0 X+1 1 X^3+X^2+1 1 X^3+X+1 X^3 1 0 0 0 X^2 0 X^3+X^2 X^2 X^2 0 X^3+X^2 X^3+X^2 0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 0 X^3 X^2 0 X^3+X^2 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3+X^2 X^2 0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^2 0 X^2 X^2 X^2 X^3+X^2 X^3 X^2 0 X^3 X^3+X^2 0 X^3+X^2 X^2 X^2 0 X^3 X^2 X^2 X^3 X^3 0 X^3+X^2 X^2 0 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^3 0 X^3+X^2 X^2 X^2 X^3+X^2 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 0 X^3 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 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+128x^77+421x^78+260x^79+672x^80+304x^81+586x^82+412x^83+591x^84+172x^85+344x^86+82x^87+63x^88+36x^89+1x^90+12x^91+1x^92+2x^94+2x^95+4x^98+1x^114+1x^118 The gray image is a linear code over GF(2) with n=656, k=12 and d=308. This code was found by Heurico 1.16 in 0.859 seconds.