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  X  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^3  0  1  1  X  0
 0  X  0  X X^3 X^3 X^3+X X^3+X X^2 X^2+X X^2 X^3+X^2+X X^3+X^2 X^2+X X^2+X X^2 X^3+X^2 X^3+X^2+X X^3+X  0 X^3+X  0 X^2+X X^2 X^3 X^3+X X^3+X^2+X X^2 X^3 X^3+X^2+X X^2  X  0 X^3+X  0 X^3+X^2+X X^3+X^2+X X^3  X X^3 X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2  X X^3+X X^3+X  X X^3+X  0 X^2+X  0 X^3+X^2 X^3+X^2  X X^3+X^2+X X^2 X^2  0  X X^3 X^2+X  X X^3+X^2  0 X^2+X X^3+X^2+X  X X^2+X X^3+X^2 X^3+X^2 X^3+X^2+X  X X^3+X X^2+X  X  X  0 X^3+X^2 X^2  X
 0  0  X  X X^2 X^3+X^2+X X^2+X X^3+X^2 X^2 X^2+X  X X^3+X^2 X^3+X^2+X X^3 X^3+X  0  X X^3 X^3+X^2+X  0  X X^3+X^2 X^3+X^2 X^2+X X^3+X^2+X X^2  X X^3 X^3+X X^2+X X^2 X^3 X^2+X X^3+X^2+X X^3 X^3 X^2 X^2 X^3+X  X X^3+X^2 X^3+X X^3+X^2+X X^3+X^2 X^3+X^2+X  0 X^3+X X^3+X^2  0 X^3+X^2+X X^2  0 X^3+X^2+X X^3+X X^3+X^2 X^3 X^3+X X^2+X X^3+X^2+X X^3+X^2 X^3+X^2+X  X  X  0  0 X^3+X^2 X^3 X^2 X^2 X^3+X X^2  X  X  0  0 X^3+X X^3+X X^3 X^3+X^2 X^3+X^2+X X^2 X^2  X X^2+X
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  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  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3

generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+170x^80+96x^81+283x^82+232x^83+535x^84+232x^85+243x^86+56x^87+141x^88+24x^89+33x^90+1x^94+1x^156

The gray image is a linear code over GF(2) with n=672, k=11 and d=320.
This code was found by Heurico 1.16 in 0.734 seconds.