The generator matrix

 1  0  1  1
 0  1  1 18
 0  0 24 21

generates a code of length 4 over Z27 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+54x^4+624x^6+216x^7+4212x^8+1232x^9+216x^10+6x^12

The gray image is a code over GF(3) with n=36, k=8 and d=12.
This code was found by Heurico 1.16 in 0.00124 seconds.