The generator matrix

 1  0  1  1  1  1
 0  1 16 26 21  4

generates a code of length 6 over Z27 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+120x^10+24x^11+328x^12+240x^13+12x^14+4x^15

The gray image is a code over GF(3) with n=54, k=6 and d=30.
This code was found by Heurico 1.16 in 0.000162 seconds.