The generator matrix

 1  0  1  1  1  1  1  1  1
 0  1  1  8  0  0  0  0  0
 0  0  6  0  0  0  0  3  0
 0  0  0  3  0  0  0  3  0
 0  0  0  0  3  0  0  3  0
 0  0  0  0  0  3  0  6  0
 0  0  0  0  0  0  3  6  0

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

Homogenous weight enumerator: w(x)=1x^0+60x^6+228x^9+720x^12+1284x^15+4374x^16+1656x^18+8748x^19+1656x^21+870x^24+86x^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 0.0562 seconds.