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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+212x^86+144x^88+104x^90+24x^92+20x^94+1x^96+4x^100+2x^104

The gray image is a linear code over GF(2) with n=352, k=9 and d=172.
This code was found by Heurico 1.16 in 97.4 seconds.