The generator matrix

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

generates a code of length 9 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+54x^15+618x^18+54x^21+2x^27

The gray image is a code over GF(3) with n=81, k=6 and d=45.
This code was found by Heurico 1.16 in 0.000562 seconds.