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

generates a code of length 41 over Z27 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+14x^81+216x^82+6x^84+6x^96

The gray image is a code over GF(3) with n=369, k=5 and d=243.
This code was found by Heurico 1.16 in 0.0154 seconds.