The generator matrix

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

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+450x^56+576x^57+720x^58+1566x^59+3684x^60+2880x^61+4434x^62+10546x^63+8262x^64+6708x^65+10674x^66+4032x^67+2304x^68+1320x^69+144x^70+462x^71+154x^72+114x^74+18x^75

The gray image is a linear code over GF(3) with n=288, k=10 and d=168.
This code was found by Heurico 1.16 in 20.8 seconds.