The generator matrix

 1  1  1  1  1  1
 0  3  0  0 21  9
 0  0  3  0 15  9
 0  0  0  3 15  6

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

Homogenous weight enumerator: w(x)=1x^0+62x^6+78x^7+270x^8+230x^9+792x^10+1080x^11+14178x^12+1422x^13+1080x^14+346x^15+138x^16+6x^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 0.0306 seconds.