The generator matrix
1 0 1 1
0 1 2X+4 0
0 0 3 0
0 0 0 6
generates a code of length 4 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+8x^3+72x^4+456x^6+288x^7+4536x^8+896x^9+288x^10+16x^12
The gray image is a code over GF(3) with n=36, k=8 and d=9.
This code was found by Heurico 1.16 in 0.00127 seconds.