The generator matrix

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

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+348x^56+264x^57+54x^58+738x^59+990x^60+324x^61+2418x^62+2308x^63+3564x^64+3834x^65+2486x^66+432x^67+918x^68+324x^69+372x^71+166x^72+120x^74+20x^75+2x^84

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 1.93 seconds.