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

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+50x^82+88x^83+136x^84+56x^85+84x^86+24x^87+22x^88+8x^89+14x^90+16x^91+4x^92+2x^96+4x^98+2x^100+1x^104

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 0.228 seconds.