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

generates a code of length 30 over Z27 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+156x^56+110x^57+216x^58+258x^59+708x^60+432x^61+138x^62+36x^63+60x^65+26x^66+30x^68+6x^69+6x^71+2x^72+2x^84

The gray image is a code over GF(3) with n=270, k=7 and d=168.
This code was found by Heurico 1.16 in 0.0168 seconds.