The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+86x^27+384x^30+972x^32+612x^33+114x^36+12x^39+6x^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 0.00636 seconds.