The generator matrix

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

generates a code of length 9 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+252x^12+1368x^15+16224x^18+1800x^21+36x^24+2x^27

The gray image is a code over GF(3) with n=81, k=9 and d=36.
This code was found by Heurico 1.16 in 0.0924 seconds.