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

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

Homogenous weight enumerator: w(x)=1x^0+108x^121+162x^122+48x^123+324x^125+24x^126+54x^130+4x^132+2x^135+2x^159

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 0.322 seconds.