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

generates a code of length 39 over Z27 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+436x^72+108x^74+640x^75+324x^76+432x^77+2686x^78+648x^79+432x^80+416x^81+236x^84+176x^87+18x^90+6x^93+2x^108

The gray image is a code over GF(3) with n=351, k=8 and d=216.
This code was found by Heurico 1.16 in 0.399 seconds.