The generator matrix

 1  0  0  1  1  1  1  1  1  1 21 18  1  1  1  1 21 18  1  1 21  1  1  0  1  1  1  1  1  1
 0  1  0  1 15 17  1 17 24 25  1  1 23  0  4 18  3  1 22 22  1 26  1  1  0  5 16 21  6  0
 0  0  1 26 16 20  1 21  2 24 10 17  1 25  8 24  1 10 16 14 12  2 15 15 23 22 18 21  7  0
 0  0  0 24 15 24  9  0 21  3 12 21  3 21  9 15  6 15 12 21 24  9 18  3  6  9 24 18 18  6

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

Homogenous weight enumerator: w(x)=1x^0+212x^51+324x^52+1572x^53+2660x^54+4464x^55+8502x^56+10896x^57+16692x^58+24408x^59+27132x^60+28668x^61+24846x^62+14648x^63+6966x^64+3702x^65+990x^66+192x^67+144x^68+76x^69+42x^70+6x^71+4x^72

The gray image is a code over GF(3) with n=270, k=11 and d=153.
This code was found by Heurico 1.16 in 25.4 seconds.