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

generates a code of length 62 over Z27 who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+96x^121+144x^122+10x^123+78x^124+288x^125+8x^126+96x^127+6x^129+2x^168

The gray image is a code over GF(3) with n=558, k=6 and d=363.
This code was found by Heurico 1.16 in 0.0997 seconds.