The generator matrix

 1  0  1  1  1  1
 0  1  1  0 26  0
 0  0 24 21  0  9
 0  0  0 18 18 18

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

Homogenous weight enumerator: w(x)=1x^0+42x^6+18x^7+162x^8+238x^9+2106x^10+648x^11+11304x^12+4158x^13+648x^14+318x^15+36x^16+4x^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 0.0179 seconds.