The generator matrix

 1  0  0  0  1  1  1 15  1  1  1  1 21  1  1  1 18  1 18 12  1  1  1  1 15  1  1  1  1
 0  1  0  0 18  1 19  1 21  3 14  4  1 17 13 11  6  8  1  6 21  2 19 11  1  0 13 17 15
 0  0  1  0 16 25 14 16  1  2 10 12 14 26 16 22  1  5 14  1  3 24 20  0 18  8  3 25 20
 0  0  0  1 14  9  5 17 16  6 15 26 26 25  1 11 19 24 12 14  7  5 25  1 10  8 13 22 13

generates a code of length 29 over Z27 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+510x^49+906x^50+4546x^51+8226x^52+10626x^53+27770x^54+34026x^55+45372x^56+80014x^57+81450x^58+75558x^59+84038x^60+45696x^61+18444x^62+10806x^63+3018x^64+204x^65+96x^66+84x^67+36x^68+6x^69+6x^70+2x^75

The gray image is a code over GF(3) with n=261, k=12 and d=147.
This code was found by Heurico 1.16 in 197 seconds.