The generator matrix

 1  1  1  1  1  3  1  1  1
 0  3 24  0 21  3 24  0 21
 0  0  9  0  0  0  9  0 18
 0  0  0  9  0  0 18  9 18
 0  0  0  0 18  0 18 18 18
 0  0  0  0  0 18 18 18  0

generates a code of length 9 over Z27 who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+30x^9+192x^12+162x^14+786x^15+1944x^16+648x^17+10236x^18+3888x^19+648x^20+1050x^21+78x^24+20x^27

The gray image is a code over GF(3) with n=81, k=9 and d=27.
This code was found by Heurico 1.16 in 0.0601 seconds.