The generator matrix

 1  0  0  1  1  1
 0  1  0 16 15  1
 0  0  1 14 16  1

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

Homogenous weight enumerator: w(x)=1x^0+306x^8+60x^9+2322x^10+1224x^11+9840x^12+4644x^13+1224x^14+60x^15+2x^18

The gray image is a code over GF(3) with n=54, k=9 and d=24.
This code was found by Heurico 1.16 in 0.0261 seconds.