The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+20x^27+78x^30+486x^32+124x^33+8x^36+8x^42+4x^45

The gray image is a code over GF(3) with n=144, k=6 and d=81.
This code was found by Heurico 1.16 in 0.0016 seconds.