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

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

Homogenous weight enumerator: w(x)=1x^0+2184x^162+2x^243

The gray image is a code over GF(3) with n=729, k=7 and d=486.
This code was found by Heurico 1.16 in 0.31 seconds.