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  3  3  3  1  3  3  3  3  3  1  1  1  3  1
 0  9  0  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9  9  9  0 18  0  9 18 18 18 18  0  9  0 18
 0  0  9 18 18  9  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9 18  0  9  0 18  9  0  9 18 18 18  0  0  9

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

Homogenous weight enumerator: w(x)=1x^0+234x^72+8x^81

The gray image is a code over GF(3) with n=324, k=5 and d=216.
This code was found by Heurico 1.16 in 0.00962 seconds.