The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+144x^55+228x^56+118x^57+354x^58+456x^59+658x^60+570x^61+2046x^62+2050x^63+5106x^64+3690x^65+2090x^66+654x^67+582x^68+102x^69+348x^70+240x^71+46x^72+96x^73+42x^74+20x^75+18x^76+6x^77+12x^78+4x^84+2x^87

The gray image is a linear code over GF(3) with n=288, k=9 and d=165.
This code was found by Heurico 1.16 in 68 seconds.