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

generates a code of length 53 over Z27 who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+54x^106+14x^108+8x^111+2x^114+2x^117

The gray image is a code over GF(3) with n=477, k=4 and d=318.
This code was found by Heurico 1.16 in 0.0398 seconds.