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

generates a code of length 83 over Z27 who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+148x^165+54x^167+6x^168+8x^171+26x^174

The gray image is a code over GF(3) with n=747, k=5 and d=495.
This code was found by Heurico 1.16 in 0.226 seconds.