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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  3  3  0  3  0  3  3  9  3  3  9  3  3  3  3  0  9  3  3  3  3  3  3 18 18 18
 0  3 24  0 21 24  9 21  6  9 12  6  9 12 24  0  3  6 18 18 21 12 15 15 18  3 15  0 21 24  0 21 24  9 12  6  9 12  6  9  0 21 12 24  6 18 18  3  3 15 15 18  3 15 21 24 21  3 24  3 12  6  3 12  6  3 21 12 24  6  3  3  3  3 15 15  3 15  3  3  3
 0  0  9  9 18 18 18  9  0  9  0  9  0  9  0 18 18 18  0  9  0 18  9 18 18  9  0  0 18  0 18  9  9  9  0 18 18  9  9  0  9  0 18 18  0  0  9 18  9  0 18 18  0  9 18  0  9  0  9  9  0 18 18  9  9  0  0 18 18  0 18  9 18  9  0  9  0 18  0  9 18

generates a code of length 81 over Z27 who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+722x^162+6x^189

The gray image is a code over GF(3) with n=729, k=6 and d=486.
This code was found by Heurico 1.16 in 0.277 seconds.