The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+29x^84+44x^85+94x^86+72x^87+12x^89+1x^96+2x^106+1x^116

The gray image is a linear code over GF(2) with n=344, k=8 and d=168.
This code was found by Heurico 1.16 in 0.34 seconds.