The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+72x^56+182x^57+180x^58+522x^59+1368x^60+720x^61+1386x^62+4744x^63+1458x^64+1872x^65+4844x^66+1008x^67+990x^68+196x^69+36x^70+18x^71+64x^72+6x^75+2x^78+4x^81+8x^84+2x^90

The gray image is a linear code over GF(3) with n=288, k=9 and d=168.
This code was found by Heurico 1.16 in 53.9 seconds.