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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+46x^82+68x^83+62x^84+84x^85+52x^86+40x^87+50x^88+40x^89+22x^90+20x^91+12x^92+4x^93+8x^94+2x^100+1x^128

The gray image is a linear code over GF(2) with n=344, k=9 and d=164.
This code was found by Heurico 1.16 in 0.477 seconds.