The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+40x^86+106x^87+112x^88+56x^89+88x^90+38x^91+27x^92+20x^93+10x^94+4x^95+2x^96+2x^100+5x^102+1x^122

The gray image is a linear code over GF(2) with n=356, k=9 and d=172.
This code was found by Heurico 1.11 in 0.204 seconds.