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

generates a code of length 73 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+558x^144+972x^146+504x^147+144x^150+6x^153+2x^216

The gray image is a code over GF(3) with n=657, k=7 and d=432.
This code was found by Heurico 1.16 in 0.5 seconds.