The generator matrix
1 1 1 X 1 1 1
0 X 2X X 0 0 0
0 0 6 0 0 0 6
0 0 0 3 0 0 6
0 0 0 0 6 0 6
0 0 0 0 0 6 3
generates a code of length 7 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+60x^6+214x^9+3558x^12+8748x^14+6618x^15+442x^18+42x^21
The gray image is a code over GF(3) with n=63, k=9 and d=18.
This code was found by Heurico 1.16 in 0.037 seconds.