The generator matrix

 1  0  1  1  1  1  1 21  1  1  1  1  1 24  1  3
 0  1  7 26 21  4 20  1 24 19 23  4 19  1 16  0
 0  0  9  0 18  9 18  0  9 18  0  0  9  9 18  9
 0  0  0  9  9 18 18  9  9  0  0  9  0  9  9 18

generates a code of length 16 over Z27 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+110x^27+324x^28+1184x^30+1296x^31+2178x^33+1296x^34+150x^36+20x^39+2x^48

The gray image is a code over GF(3) with n=144, k=8 and d=81.
This code was found by Heurico 1.16 in 0.024 seconds.