The generator matrix

 1  1  1  1  1  1  1  1  1
 0  3  0  0  0  0  0  0  3
 0  0  3  0  0  0  0  0  6
 0  0  0  3  0  0  0  0  6
 0  0  0  0  3  0  0  0  6
 0  0  0  0  0  3  0  0  6
 0  0  0  0  0  0  3  0  6
 0  0  0  0  0  0  0  3  3

generates a code of length 9 over Z9 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+72x^6+168x^9+756x^12+1260x^15+14970x^18+1512x^21+774x^24+170x^27

The gray image is a code over GF(3) with n=27, k=9 and d=6.
This code was found by Heurico 1.16 in 0.122 seconds.