The generator matrix

 1  0  0  1  1  1  1  1 24  1  1  1 15  1  1  1  9  1  1  1  1  1  1  6 15  1
 0  1  0  1 15 17  1 17  1 23 10 21  1 25 20  0  1 15  5  9 11 17 12  1  1 13
 0  0  1 26 16 20  1 21  4 25 21 17  5 26 18  6  6 20 25 19  0 16 10  0 19 18
 0  0  0 24 15 24  9  0  6 12 18  6 21  3 24 15 24 18 18 21 12  6  3  3 15 21

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

Homogenous weight enumerator: w(x)=1x^0+558x^44+702x^45+2262x^46+4356x^47+7268x^48+9252x^49+21156x^50+22770x^51+26274x^52+36000x^53+23522x^54+12714x^55+7650x^56+1748x^57+522x^58+228x^59+108x^60+6x^61+36x^62+12x^63+2x^66

The gray image is a code over GF(3) with n=234, k=11 and d=132.
This code was found by Heurico 1.16 in 21.4 seconds.