The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  1  1  1  0  1  1  1 24  1  1  1 21  1  1  1  1  1  1  1  1  1  9 12  6  1  1  1  1  9  1  1  3  1  1  1  6  1  1  1 12  1  1  1  1  1  1  1 18 15  1  1 15 18  3  1  1  0  1  1  1  1
 0  1  7 26  4 21 20  1 24 19 23  1  0 16 26  1 20 21  4  1 24 19 23  1  9 12 16 13  6 10  8 11  5  1  1  1  9 12  7  8  1 13 11  1  6 10 14  1  7  9 26  1  0 21 12 24  6 10 14  1  1 16 19  1  1  1  8  5  9  4 13 20 11
 0  0  9  0 18 18  9  9  9  0 18 18  9 18  9  9 18  0  0  0 18  9  0 18 18  9  0  9  0 18 18  0  9 18  0  9  9  0  0  9  9 18 18  0  9  0  9  0 18  0 18  9 18  9 18  0 18  9  0 18 18  9 18  9  0 18  0 18  9  9  0  0  9

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

Homogenous weight enumerator: w(x)=1x^0+1152x^144+810x^147+216x^153+8x^162

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 91.5 seconds.