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  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 21  6  0  9 21 24  0 12  6  9 12 24  9 21  9 15 12  6 18 12  6  0  0  9  9 21 21 12 12 24  6 24 15  0 21  6 18  3 24 18  6 12 18 15  3 15 24  0  9  3 21  9  3  6 12  0  9 15 18  3 24
 0  0  9  0  9  0 18 18  9 18 18  0  9  0  9  9  0  9 18  9  0 18  9  0 18 18 18  0  9  9  0 18  9  9 18 18  0 18  0 18  0  9  0 18  0 18  9  9  0  0 18 18  9 18  9  0  0 18 18  0 18 18  0  0  0  9 18
 0  0  0  9 18  9  9 18 18  9 18 18  0 18 18  9  9  9 18  9 18  9  0  0  0  0  0 18  9  0  0  0  0  9 18  9 18 18  9  0  0  0  9  9  0  9  9 18  0 18 18  0 18 18 18 18  9  0  0  9  9  9  9  0 18  0  0

generates a code of length 67 over Z27 who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+38x^129+24x^130+178x^132+84x^133+1620x^134+100x^135+36x^136+56x^138+12x^139+26x^141+6x^142+4x^144+2x^201

The gray image is a code over GF(3) with n=603, k=7 and d=387.
This code was found by Heurico 1.16 in 0.162 seconds.