The generator matrix

 1  1  1  1  1  1  1  1  1  X
 0  3  0  0  3  0  3  3  6  3
 0  0  3  0  6  3  6  3  6  0
 0  0  0  3  6  6  0  6  6  3

generates a code of length 10 over Z9[X]/(X^2+6,3X) who�s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+114x^18+486x^20+108x^21+20x^27

The gray image is a code over GF(3) with n=90, k=6 and d=54.
This code was found by Heurico 1.16 in 0.000576 seconds.