The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+48x^86+3x^88+8x^90+2x^92+1x^100+1x^108

The gray image is a linear code over GF(2) with n=344, k=6 and d=172.
This code was found by Heurico 1.16 in 0.221 seconds.