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  0  3  3  3  3  0  3  9  9  1  1  1  3
 0  3 24  0 21 24  9 21  6  9 12  6  9 12 24  0  3  6 18 18 21 12 15 15 18  3 15  0 21 24  0 21 24  9 12  6  9 12  6  9  0 21 12 24  6 21 24 21  3 24  6 12 12  3 15  3  3 18 18 18  0
 0  0  9  9 18 18 18  9  0  9  0  9  0  9  0 18 18 18  0  9  0 18  9 18 18  9  0  0 18  0 18  9  9  9  0 18 18  9  9  0  9  0 18 18  0 18  0  9  0  9 18  0  9 18 18 18  0  0  9 18  0

generates a code of length 61 over Z27 who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+372x^120+234x^123+92x^126+24x^129+4x^135+2x^144

The gray image is a code over GF(3) with n=549, k=6 and d=360.
This code was found by Heurico 1.16 in 0.202 seconds.