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

generates a code of length 24 over Z27 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+34x^45+666x^48+18x^51+8x^54+2x^72

The gray image is a code over GF(3) with n=216, k=6 and d=135.
This code was found by Heurico 1.16 in 0.00433 seconds.