The generator matrix

 1  1  1  1  1  1  1  1  1  3  3  0  1
 0  3 24  9 21  6 18 12 15 21 24  3  0

generates a code of length 13 over Z27 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+60x^24+54x^26+122x^27+6x^30

The gray image is a code over GF(3) with n=117, k=5 and d=72.
This code was found by Heurico 1.16 in 0.00046 seconds.