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 1 1 1 X^3 1 X^2+X 1 X^2 1 X 1 1 1 X X^2 1 X^3+X X^3 1 1 X 1 X^2+X 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 X X X 1 1 1 0 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 X X^3+X^2+X+1 X^2 1 X 1 X^3+X^2+1 1 1 1 X^2+X X^3+X^2+X 1 X 1 X^3+X^2 1 1 X+1 X^2 X^3+X^2+X X^3+1 1 X+1 X^2+1 X+1 X^2+X+1 X^3+X^2+1 X+1 X X^3+1 X X^3+X^2+1 X^2+X+1 X^3+X^2+1 X^3+X+1 X^3+X^2+1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2 1 1 1 X^2 X^3+X^2+X+1 X^3+X^2 1 X+1 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 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 X^3 0 X^3 X^3 X^3 X^3+X^2 0 X^3 0 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 X^3+X^2 X^2 X^2 X^3+X^2 0 X^3 X^3+X^2 0 X^3 X^2 0 X^2 X^3 X^3+X^2 X^3+X^2 X^3 0 X^3 X^2 X^3 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 X^3 0 0 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 0 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 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 0 0 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 79. Homogenous weight enumerator: w(x)=1x^0+144x^79+281x^80+560x^81+396x^82+546x^83+445x^84+458x^85+443x^86+348x^87+172x^88+184x^89+39x^90+48x^91+8x^92+10x^93+1x^94+2x^96+2x^99+2x^100+4x^101+1x^114+1x^116 The gray image is a linear code over GF(2) with n=672, k=12 and d=316. This code was found by Heurico 1.16 in 0.922 seconds.