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 X+3  X 2X+3 2X  0  3  6 X+3 2X+3 X+6 X+3 2X+3 2X  3 2X+3  3  3 2X  X 2X+3 2X+3  6 X+3  6 2X+6 2X X+3
 0  0  X 2X  0 2X+3  X X+3 2X  6 X+3 2X 2X+6  X  X  3  6 2X+3 X+3 X+6  6  6  3 X+6  6  X  3  X  X X+3  3  X
 0  0  0  6  0  3  3  6  0  0  0  6  6  0  6  3  3  3  6  6  3  6  6  3  3  0  0  0  3  3  0  6
 0  0  0  0  6  3  6  0  3  3  3  3  6  0  0  3  6  0  6  6  0  3  3  6  3  6  6  6  0  0  0  3

generates a code of length 32 over Z9[X]/(X^2+3,3X) 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 code over GF(3) with n=288, k=9 and d=165.
This code was found by Heurico 1.16 in 68.4 seconds.