The generator matrix

 1  0  0  1  1  1
 0  1  0  7  3  0
 0  0  1 14  2  0
 0  0  0  9 18  9

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

Homogenous weight enumerator: w(x)=1x^0+94x^6+24x^7+810x^8+564x^9+5490x^10+3240x^11+33828x^12+10980x^13+3240x^14+740x^15+30x^16+8x^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 0.131 seconds.