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  1  1  1  1  1  1  1  1  X  X  0  X X^2  0  X  X  0 X^2  0  X  0  X  0  X  X X^2  0  X X^2 X^2  X  X  X  X  X  X  1  1  1  1  0  0 X^2  X  X  X  X  1  1  1  1 X^2 X^2  0 X^2 X^2 X^2 X^2  1  1  X  X  1
 0  X  0  X  0  0 X^2+X X^2+X  0  0  X  X  0  0 X^2+X X^2+X X^2 X^2  X X^2+X X^2 X^2 X^2+X  X X^2 X^2  X X^2+X X^2 X^2 X^2+X  X X^2  X  X X^2+X  X  0  0  X  X X^2  X X^2+X  X X^2+X  0  X  X X^2  X X^2+X  X  X X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  X  X  0  0 X^2 X^2  0 X^2+X X^2+X  X  X  X  X  X  0  X  X  X X^2  0  0 X^2  0
 0  0  X  X  0 X^2+X X^2+X  0 X^2 X^2+X X^2+X X^2 X^2  X  X X^2 X^2  X  X  0 X^2  X X^2+X X^2  0 X^2+X X^2+X X^2  0 X^2+X  X  0  X  X X^2  0  X  X X^2+X X^2+X X^2+X  X  0 X^2 X^2  0  X  X X^2+X  X  0 X^2  X X^2+X  X  X  0 X^2 X^2  0  0 X^2 X^2  0  X X^2+X  0  X X^2+X X^2+X X^2+X  0 X^2 X^2  0 X^2 X^2+X  X X^2 X^2  0  0  X X^2+X  0 X^2  0
 0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  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+17x^84+60x^85+23x^86+94x^87+11x^88+16x^89+3x^90+16x^91+3x^92+3x^94+1x^98+4x^101+2x^102+2x^103

The gray image is a linear code over GF(2) with n=348, k=8 and d=168.
This code was found by Heurico 1.16 in 0.476 seconds.