The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1 21 24
 0  1  7 26  4 21 20 24 19 26  8 20 11  1  1
 0  0  9  0 18 18  9  0  9 18  9  0 18  0 18

generates a code of length 15 over Z27 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+170x^27+486x^28+396x^30+972x^31+144x^33+18x^36

The gray image is a code over GF(3) with n=135, k=7 and d=81.
This code was found by Heurico 1.16 in 0.507 seconds.