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

generates a code of length 30 over Z27 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+126x^53+256x^54+396x^56+68x^57+126x^59+4488x^60+522x^62+128x^63+252x^65+82x^66+36x^68+42x^69+20x^72+10x^75+6x^78+2x^84

The gray image is a code over GF(3) with n=270, k=8 and d=159.
This code was found by Heurico 1.16 in 17.8 seconds.