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

generates a code of length 62 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+16x^123+210x^124+8x^126+6x^133+2x^159

The gray image is a code over GF(3) with n=558, k=5 and d=369.
This code was found by Heurico 1.16 in 0.0724 seconds.