The generator matrix

 1  0  0  1  1  1 X+3  1  1  1  1  1  1  1 2X  0  1  1  1  1 X+3  1  1  1 2X+3  1  1  1  1  6  1
 0  1  0 2X+3  1 2X+4  1  3 2X+2  8  2 2X+7 2X X+8  1  1 X+7 X+2 X+7 X+6  1 2X+4 X+8  5 X+6 X+1  3  6 2X+3 2X+3  8
 0  0  1 2X+4  1 2X+3 2X+2 X+2  4 2X+8 X+3 2X+8  0 X+5  6 X+7 2X+5 2X X+3 X+1 X+1 2X+4 X+4  4  1 X+5 X+8 2X+5  8  1 2X+6
 0  0  0  3  3  3  0  6  0  6  3  3  6  0  3  3  0  0  6  0  6  6  3  6  6  6  3  6  0  0  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+366x^55+798x^56+2328x^57+2958x^58+3066x^59+7220x^60+7446x^61+6336x^62+12046x^63+7254x^64+4116x^65+3336x^66+1344x^67+246x^68+82x^69+60x^70+18x^71+14x^72+12x^73+2x^81

The gray image is a code over GF(3) with n=279, k=10 and d=165.
This code was found by Heurico 1.16 in 3.14 seconds.