The generator matrix
1 0 1 1 1 1 1
0 1 2X+4 8 0 0 0
0 0 3 0 0 0 6
0 0 0 6 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+114x^6+646x^9+7770x^12+34992x^14+14178x^15+1306x^18+42x^21
The gray image is a code over GF(3) with n=63, k=10 and d=18.
This code was found by Heurico 1.16 in 0.16 seconds.