The generator matrix
1 0 0 1 1
0 1 0 1 6
0 0 1 8 6
0 0 0 2X X+6
generates a code of length 5 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+114x^4+1820x^6+684x^7+18792x^8+7220x^9+102780x^10+37584x^11+7230x^12+912x^13+10x^15
The gray image is a code over GF(3) with n=45, k=11 and d=12.
This code was found by Heurico 1.16 in 0.649 seconds.