The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^27+162x^30+1458x^32+324x^33+114x^36+12x^45

The gray image is a code over GF(3) with n=144, k=7 and d=81.
This code was found by Heurico 1.16 in 0.161 seconds.