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

generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+11x^82+28x^83+52x^84+336x^85+50x^86+12x^87+10x^88+8x^89+1x^90+1x^104+2x^118

The gray image is a linear code over GF(2) with n=680, k=9 and d=328.
This code was found by Heurico 1.16 in 0.688 seconds.