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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+2x^86+20x^87+2x^88+4x^89+1x^90+1x^92+1x^94

The gray image is a linear code over GF(2) with n=340, k=5 and d=172.
This code was found by Heurico 1.16 in 0.319 seconds.