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

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 0.236 seconds.