The generator matrix

 1  0  0  0  1  1  1 18  1  1  1 21  1  1  1 24  1  1  1 15  1  1  3  1  9  1  0  1  1  1
 0  1  0  0 18  1 19  1  3  6  4  1  8 21 14  1  7 22 11  1 21 16  3 21  1  8  1 20 18 18
 0  0  1  0 16 25 14  7  4  2 24  8  1 11  9 17  8 13 19 22 23  6  1  3 18 26 24 23  1  4
 0  0  0  1 14  9  5  5 25 24 22  4 15 10  1  6 13  8 16 22 11 26  7 17 25  5 11 19  3 20

generates a code of length 30 over Z27 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+666x^51+1098x^52+4728x^53+9178x^54+10920x^55+24582x^56+38786x^57+46326x^58+69810x^59+90910x^60+75378x^61+72432x^62+52156x^63+19482x^64+11058x^65+3302x^66+330x^67+102x^68+122x^69+42x^70+24x^71+6x^72+2x^75

The gray image is a code over GF(3) with n=270, k=12 and d=153.
This code was found by Heurico 1.16 in 207 seconds.