The generator matrix

 1  0  1  1  1  1  1  3  1  1  1 X+3 2X  1  1  1 2X 2X  1  1  1  6  1  1  1  1  1  1  X  1  1
 0  1  1  8 X+3 X+2 2X+4  1  8 2X X+1  1  1  3 X+2 2X+1  1  1 2X+8 2X 2X+3  1 2X+3 X+4 2X+8 X+3 X+3 2X+4 X+6 2X+8  7
 0  0 2X  0  3  3 2X+3 X+3 2X+3  3 2X 2X+3 2X+3 X+6 2X+6 X+6  6 2X  0 2X  X  6 X+3 X+6 2X+3  3 2X+6  3 2X  0 2X
 0  0  0  6  6  0  3  6  6  3  6  0  3  0  3  3  6  6  3  6  3  3  6  0  0  0  3  6  0  6  3

generates a code of length 31 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+96x^55+306x^56+658x^57+1092x^58+1446x^59+1642x^60+2808x^61+3168x^62+2284x^63+2928x^64+1776x^65+908x^66+312x^67+48x^68+86x^69+54x^70+54x^71+8x^72+6x^74+2x^81

The gray image is a code over GF(3) with n=279, k=9 and d=165.
This code was found by Heurico 1.16 in 0.475 seconds.