The generator matrix

 1  0  0  0  1  1  1  1  1  1 24 18  6  1  1  1  1  1  1 12  1 15  1  1 18  1  1
 0  1  0  0 18 19 21 12 25 23  1  1  1 16 10  0 17  8  7  1  1  1 23 21  1 26  6
 0  0  1  0 16 19  7 23  2  3 22  2 21 19 24 15  8 12 13 23  5  6 26 17 11  4 15
 0  0  0  1 14 21 25 18 26  1 23  8  1 10 13  7 23 17 11  6 10 26  7 10 11  6 25

generates a code of length 27 over Z27 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+316x^45+1062x^46+3708x^47+7660x^48+9558x^49+25362x^50+33056x^51+51636x^52+73182x^53+87266x^54+87810x^55+76272x^56+45504x^57+17190x^58+9486x^59+1828x^60+384x^61+60x^62+50x^63+30x^64+12x^65+8x^66

The gray image is a code over GF(3) with n=243, k=12 and d=135.
This code was found by Heurico 1.16 in 180 seconds.