The generator matrix

 1  1  1  1  1  1  1  1  1  3  3  3  3  1  1  1
 0  9  0  0  0  0  0  9  9  9  9  9  0  0  0  9
 0  0  9  0  0  0  9 18 18  9  9  0  9  0  0 18
 0  0  0  9  0  0 18 18  9  0  9 18  0  0  9 18
 0  0  0  0  9  0 18  9 18  9  0 18  0  9 18 18
 0  0  0  0  0  9  9  0  9  9 18 18  9 18 18  9

generates a code of length 16 over Z27 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+24x^21+80x^24+328x^27+428x^30+4374x^32+776x^33+446x^36+80x^39+8x^42+8x^45+8x^48

The gray image is a code over GF(3) with n=144, k=8 and d=63.
This code was found by Heurico 1.16 in 0.0448 seconds.