The generator matrix

 1  0  1  1  1  1
 0  1  1 26  0 18
 0  0 24  0  3 18
 0  0  0  3  3 12

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

Homogenous weight enumerator: w(x)=1x^0+102x^6+54x^7+486x^8+490x^9+7290x^10+1944x^11+31518x^12+14418x^13+1944x^14+690x^15+108x^16+4x^18

The gray image is a code over GF(3) with n=54, k=10 and d=18.
This code was found by Heurico 1.16 in 0.145 seconds.