The generator matrix

 1  1  1  1  1  1
 0  3  0 21  0  3
 0  0  3  6 24  3
 0  0  0  9  0 18
 0  0  0  0  9  9

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

Homogenous weight enumerator: w(x)=1x^0+66x^6+486x^8+256x^9+1944x^11+14616x^12+1944x^14+348x^15+22x^18

The gray image is a code over GF(3) with n=54, k=9 and d=18.
This code was found by Heurico 1.16 in 0.0319 seconds.