The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+83x^84+48x^85+136x^86+48x^87+91x^88+16x^89+40x^90+16x^91+27x^92+1x^96+2x^104+2x^108+1x^128

The gray image is a linear code over GF(2) with n=348, k=9 and d=168.
This code was found by Heurico 1.16 in 0.489 seconds.