The generator matrix

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

generates a code of length 80 over Z27 who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+80x^162

The gray image is a code over GF(3) with n=720, k=4 and d=486.
This code was found by Heurico 1.16 in 0.195 seconds.