The generator matrix

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

generates a code of length 30 over Z27 who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+234x^60+4x^63+4x^72

The gray image is a code over GF(3) with n=270, k=5 and d=180.
This code was found by Heurico 1.16 in 0.00506 seconds.