The generator matrix

 1  0  0  1  1  1 15  1  1  1  3  1  1 21  1  6  1  1  1 18 24  1  1  1  1  1  9  1  1
 0  1  0  1 15 26  1 19 20 18  1 17 16  1 18  1 20  2  4  1  3 17 12  7  6 18  1 24 24
 0  0  1 26 16 26 22 19 21 20 23 19 15  9 22 11 12 25  0 16  1  8  9 20 11  5 13 12  0
 0  0  0 24 15  9  3 21  3  6 12 15 18 24 21  9  6  9  3 24 15 21 21  9 18  3 24 24  0

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

Homogenous weight enumerator: w(x)=1x^0+162x^49+342x^50+1484x^51+2634x^52+4014x^53+7634x^54+12498x^55+17610x^56+20978x^57+29508x^58+30708x^59+22110x^60+16638x^61+6372x^62+3276x^63+696x^64+210x^65+148x^66+66x^67+36x^68+16x^69+6x^70

The gray image is a code over GF(3) with n=261, k=11 and d=147.
This code was found by Heurico 1.16 in 24.3 seconds.