The generator matrix

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

generates a code of length 15 over Z27 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+36x^29+186x^30+18x^32+2x^45

The gray image is a code over GF(3) with n=135, k=5 and d=87.
This code was found by Heurico 1.16 in 0.00166 seconds.