The generator matrix
1 1 1 1 1
0 3 0 0 0
0 0 3 0 0
0 0 0 3 0
0 0 0 0 3
generates a code of length 5 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+10x^3+40x^6+80x^9+1944x^10+80x^12+32x^15
The gray image is a code over GF(3) with n=45, k=7 and d=9.
This code was found by Heurico 1.16 in 0.000457 seconds.