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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+96x^82+32x^83+114x^84+64x^85+90x^86+32x^87+54x^88+20x^90+6x^92+2x^94+1x^160

The gray image is a linear code over GF(2) with n=340, k=9 and d=164.
This code was found by Heurico 1.16 in 7.65 seconds.