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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+172x^87+88x^88+108x^89+16x^90+64x^91+9x^92+16x^93+20x^95+9x^96+4x^97+2x^100+2x^104+1x^108

The gray image is a linear code over GF(2) with n=356, k=9 and d=174.
This code was found by Heurico 1.16 in 17.4 seconds.