The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+20x^85+99x^86+24x^87+75x^88+20x^89+11x^90+2x^92+1x^98+1x^100+1x^102+1x^116

The gray image is a linear code over GF(2) with n=348, k=8 and d=170.
This code was found by Heurico 1.11 in 0.281 seconds.