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

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

Homogenous weight enumerator: w(x)=1x^0+12x^72+192x^74+136x^75+360x^77+982x^78+360x^80+12x^81+24x^83+60x^84+36x^86+8x^87+2x^90+2x^111

The gray image is a code over GF(3) with n=351, k=7 and d=216.
This code was found by Heurico 1.16 in 0.034 seconds.