The generator matrix

 1  1  1  1  1  1  1  1  3  3  3  1
 0  9 18  0  9 18  0  9  9 18  0 18

generates a code of length 12 over Z27 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+72x^24+8x^27

The gray image is a code over GF(3) with n=108, k=4 and d=72.
This code was found by Heurico 1.16 in 0.00031 seconds.