The generator matrix

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

generates a code of length 6 over Z27 who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+26x^9+108x^10+348x^12+216x^13+30x^15

The gray image is a code over GF(3) with n=54, k=6 and d=27.
This code was found by Heurico 1.16 in 0.00028 seconds.