The generator matrix

 1  0  1  1  1  1
 0  1  1  0 25  0
 0  0 24 21  3 24
 0  0  0 18  0  9
 0  0  0  0  9 18

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

Homogenous weight enumerator: w(x)=1x^0+138x^6+486x^8+688x^9+6804x^10+1944x^11+32490x^12+13608x^13+1944x^14+924x^15+22x^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 0.148 seconds.