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

generates a code of length 72 over Z27 who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+156x^141+1932x^144+36x^147+60x^150+2x^216

The gray image is a code over GF(3) with n=648, k=7 and d=423.
This code was found by Heurico 1.16 in 0.159 seconds.