The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  1  1  1
 0  1 16 26 21  4 20  1 24 19 23  1  9  7 12

generates a code of length 15 over Z27 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+168x^28+120x^29+38x^30+336x^31+60x^32+2x^33+4x^36

The gray image is a code over GF(3) with n=135, k=6 and d=84.
This code was found by Heurico 1.16 in 0.000739 seconds.