The generator matrix

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

generates a code of length 16 over Z27 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+38x^30+162x^32+24x^33+14x^36+4x^39

The gray image is a code over GF(3) with n=144, k=5 and d=90.
This code was found by Heurico 1.16 in 0.000764 seconds.