The generator matrix

 1  1  1  1  1  1  1  X  1  1  X  X
 0  X  0  0 2X X+3  X X+3 2X+3 2X X+3 X+3
 0  0  X 2X  0 2X+3 X+6 2X+3 X+3 2X+6 2X+3 2X+6
 0  0  0  6  0  3  3  3  6  0  6  0
 0  0  0  0  6  6  3  0  3  0  6  3

generates a code of length 12 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+624x^18+2268x^21+13446x^24+3176x^27+162x^30+6x^36

The gray image is a code over GF(3) with n=108, k=9 and d=54.
This code was found by Heurico 1.16 in 18.8 seconds.