The generator matrix

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

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+99x^80+340x^81+156x^82+444x^83+148x^84+290x^85+135x^86+252x^87+84x^88+80x^89+10x^90+1x^92+2x^93+1x^94+1x^98+2x^100+1x^114+1x^116

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 0.719 seconds.