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

generates a code of length 72 over Z27 who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+128x^135+420x^138+466x^141+1458x^142+438x^144+2916x^145+276x^147+160x^150+142x^153+96x^156+58x^159+2x^207

The gray image is a code over GF(3) with n=648, k=8 and d=405.
This code was found by Heurico 1.16 in 0.462 seconds.