The generator matrix

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

generates a code of length 11 over Z27 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+30x^20+2x^21+144x^22+60x^23+4x^24+2x^30

The gray image is a code over GF(3) with n=99, k=5 and d=60.
This code was found by Heurico 1.16 in 0.000324 seconds.