The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^6+18x^7+54x^8+130x^9+324x^10+216x^11+4770x^12+594x^13+216x^14+174x^15+36x^16+4x^18

The gray image is a code over GF(3) with n=54, k=8 and d=18.
This code was found by Heurico 1.16 in 0.00385 seconds.