The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  1 X^2 X^2+X X^2+X  0  1  1  X  0  1  1  1  1  1 X^2  0  1 X^2+X  X  1  X  1  1  1  X  1 X^2+X  1  1 X^2  1  1 X^2  1  0  1 X^2  1  1 X^2+X  1  X X^2  1  1  0  X  1 X^2 X^2+X  0  X  1  1  X  1 X^2+X X^2+X  1  1  1  1  X  1 X^2  0 X^2  X  1  X  1 X^2+X  1  1
 0  1  0  1 X^2 X^2+1  1  1 X^2+X X^2+1  0 X^2  1  1  0  X  X X+1  1  1 X^2+X+1  X  X  X X^2+X+1  1  1 X+1  1  0 X^2  1  1 X^2+X X^2+1  1  0  1 X+1 X^2+X  0  1 X^2+X+1  1 X+1  1  0  1 X^2+1 X^2+X+1  1 X^2+X X^2+X  X X^2+X X^2+X X^2+X  X X^2+X X^2+X  X X^2 X^2 X^2 X+1  1 X^2  1 X^2 X^2+1 X^2+1 X^2+X+1  0  0 X^2 X^2  1  1  1  0  1 X+1  1 X+1  1
 0  0  1 X^2  1 X^2+1 X^2+1 X^2+X  1 X+1  X X^2+X+1  X X+1  1  1  0 X^2  0  1  1  1 X+1  X X^2+X  0 X^2+X+1 X+1 X^2+1  1 X^2+1  X X^2+X+1 X^2+1  X X^2+X+1 X^2 X^2 X^2+X X+1  1 X^2+1  0 X^2+1  1 X^2+X X^2+X X^2+X+1 X^2 X^2+X+1  X  X  1  1 X^2+X  0  1  1 X^2  1  1  1  1  0  X  1  X X^2+X  1 X^2+X  0 X^2 X^2+X+1  X X^2  1 X^2+1 X+1 X+1  1 X^2+X X^2+X+1 X^2+X+1  0  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+38x^82+92x^83+100x^84+114x^85+54x^86+56x^87+12x^88+26x^89+6x^90+5x^92+1x^94+1x^96+5x^98+1x^112

The gray image is a linear code over GF(2) with n=340, k=9 and d=164.
This code was found by Heurico 1.11 in 0.172 seconds.