The generator matrix

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

generates a code of length 15 over Z27 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+186x^24+162x^26+452x^27+486x^28+648x^29+2286x^30+972x^31+648x^32+630x^33+78x^36+12x^42

The gray image is a code over GF(3) with n=135, k=8 and d=72.
This code was found by Heurico 1.16 in 11.8 seconds.