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

generates a code of length 67 over Z27 who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+80x^126+164x^129+624x^132+1096x^135+92x^138+70x^141+26x^144+14x^147+4x^150+6x^153+4x^159+6x^162

The gray image is a code over GF(3) with n=603, k=7 and d=378.
This code was found by Heurico 1.16 in 0.143 seconds.