The generator matrix

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

generates a code of length 26 over Z27 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+264x^44+210x^45+162x^46+678x^47+786x^48+972x^49+1920x^50+1746x^51+4860x^52+3210x^53+1946x^54+1296x^55+834x^56+312x^57+348x^59+72x^60+36x^62+12x^63+18x^66

The gray image is a code over GF(3) with n=234, k=9 and d=132.
This code was found by Heurico 1.16 in 92.7 seconds.