The generator matrix

 1  0  0  0  1  1  1 2X+3  1  1 X+3 X+6
 0  1  0  0 2X+3  4 2X+1  1 2X+6 2X+4  1  1
 0  0  1  0 2X+4  4 2X+8 X+4 2X+3 X+2 2X+6 X+2
 0  0  0  1 2X+2 X+3 X+8 X+2 2X+1 X+7 X+5  3

generates a code of length 12 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+132x^17+2556x^18+1938x^19+14370x^20+12624x^21+71136x^22+56700x^23+154506x^24+139626x^25+56802x^26+17594x^27+3084x^28+300x^29+66x^30+6x^33

The gray image is a code over GF(3) with n=108, k=12 and d=51.
This code was found by Heurico 1.16 in 41.3 seconds.