The generator matrix
1 1 1 1 1
0 3 0 0 3
0 0 3 0 6
0 0 0 3 6
generates a code of length 5 over Z9 who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+20x^6+20x^9+162x^10+30x^12+10x^15
The gray image is a code over GF(3) with n=15, k=5 and d=6.
This code was found by Heurico 1.16 in 7.8e-005 seconds.