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  0  X X^3+X^2  X  0  X X^3+X^2  X  0  X X^3+X^2  X  X  X  X  X X^3  X X^2  X  X  1  1  X  X  X  X  X  X  1  1  X  X  X  X  1  X  X  X  X  1  X  X  1  1  X  1  1  1  1  1  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2  X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2 X^3+X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2 X^3+X X^2+X  X X^3+X  X X^2+X  X X^3+X  X X^2+X  X X^3+X  X  0 X^3+X^2  0 X^3+X^2 X^2+X  X X^3+X  X  0 X^3+X^2  0 X^3 X^3 X^2 X^3 X^2 X^2 X^3 X^2+X X^3+X X^3+X^2+X  X X^3+X^2+X  X X^3+X^2 X^3+X^2+X  X  X X^3+X^2+X X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^2  0  0 X^3 X^3  0 X^3+X^2
 0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3
 0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 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  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0  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 83.

Homogenous weight enumerator: w(x)=1x^0+84x^83+75x^84+220x^85+32x^86+76x^87+14x^88+4x^89+3x^92+1x^104+2x^108

The gray image is a linear code over GF(2) with n=680, k=9 and d=332.
This code was found by Heurico 1.16 in 73.1 seconds.