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 X^3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2 X^2 X^2
 0  X  0 X^3+X^2+X X^3 X^2+X X^3 X^3+X  0 X^2+X X^3 X^3+X X^3 X^2+X X^3 X^3+X X^3 X^2+X  X  0  0 X^3+X  0 X^3+X^2+X X^3 X^3+X^2+X X^3 X^3+X X^3 X^3+X^2+X X^3 X^3+X X^2 X^2+X X^3+X^2  X X^2 X^2+X X^3+X X^2 X^2 X^2+X X^3+X^2 X^3+X X^3+X^2  X X^2 X^2+X X^3+X^2+X X^2 X^2 X^3+X^2+X X^3+X X^3+X^2  X X^2 X^3+X X^2 X^2+X X^3+X^2 X^2 X^3+X^2 X^2+X  X X^3  0 X^2 X^3 X^3+X^2 X^2+X  X X^3+X^2+X X^3+X X^3  0  0 X^3 X^3+X^2+X X^2+X X^3+X^2+X X^2+X X^3+X^2 X^3+X^2  0
 0  0 X^3+X^2  0  0 X^3+X^2 X^2 X^2  0  0  0  0 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3 X^2 X^3 X^3 X^3+X^2 X^3 X^2 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^2 X^3+X^2  0 X^2 X^3 X^3 X^2  0  0 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2 X^3 X^3  0 X^3 X^3 X^3 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2  0 X^2  0 X^2 X^3 X^3+X^2 X^3  0 X^2 X^3+X^2  0 X^2 X^2  0  0  0 X^3
 0  0  0 X^3+X^2 X^2 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3  0 X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^3  0  0  0 X^3+X^2 X^3+X^2 X^2 X^3 X^2  0 X^3  0  0 X^3+X^2 X^3+X^2 X^2 X^2  0 X^3 X^2  0 X^3 X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3  0 X^3+X^2  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2  0 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+254x^80+128x^81+152x^82+256x^83+296x^84+640x^85+48x^86+208x^88+56x^90+8x^92+1x^160

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 1.48 seconds.