The generator matrix

 1  0  1  1  1  1  1 18  1 24  1  1  1  1  0  1  1  1  6  1  1  3  1  1 24  1  1
 0  1  1 26  0 25 17  1 18  1 25  2  9 16  1 14 25  3  1 16  5  6  1 10  1  5  0
 0  0 24  0  9  3 21  3 21  6 12 21  3  6 21 24  6  9  9  9  0 24  0  3 12 12  9
 0  0  0  3 15  9 15 15  9  0  6 18  6  6 12 21 21 21  3 24  9 18 21 12 12 21  9

generates a code of length 27 over Z27 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+234x^46+384x^47+1032x^48+1200x^49+2370x^50+4284x^51+5082x^52+6798x^53+12746x^54+8970x^55+7008x^56+5664x^57+1716x^58+852x^59+288x^60+246x^61+78x^62+42x^63+48x^64+6x^65

The gray image is a code over GF(3) with n=243, k=10 and d=138.
This code was found by Heurico 1.16 in 4.57 seconds.