The generator matrix

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

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+54x^84+100x^85+24x^86+34x^88+24x^89+2x^90+4x^92+4x^93+4x^94+1x^96+2x^98+2x^100

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.