The generator matrix

 1  0  1  1  1  1  1 21  1  1  1  9  1  1  1 12  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 24  6 18  3 15
 0  1 16 26 21  4 20  1  9  7  8  1 12 13 11  1 24  6 19 10 23  5 18  3 25 22 15  1 17  2 14  1  1  1  1  1

generates a code of length 36 over Z27 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+720x^72+8x^81

The gray image is a code over GF(3) with n=324, k=6 and d=216.
This code was found by Heurico 1.16 in 0.00731 seconds.