The generator matrix

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

generates a code of length 6 over Z27 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+54x^8+40x^9+216x^11+1620x^12+216x^14+36x^15+4x^18

The gray image is a code over GF(3) with n=54, k=7 and d=24.
This code was found by Heurico 1.16 in 0.00098 seconds.