The generator matrix
1 1 1 1 1 1 1 1 1 X
0 6 0 0 6 0 6 6 3 6
0 0 6 0 3 6 3 6 3 0
0 0 0 6 3 3 0 3 3 6
generates a code of length 10 over Z9[X]/(X^2+3,3X) 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.