The generator matrix
1 0 0 0 1
0 1 0 0 2X+4
0 0 1 0 2X+2
0 0 0 1 2X+2
generates a code of length 5 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+240x^4+5060x^6+1440x^7+61560x^8+20180x^9+297720x^10+123120x^11+20190x^12+1920x^13+10x^15
The gray image is a code over GF(3) with n=45, k=12 and d=12.
This code was found by Heurico 1.16 in 2.05 seconds.