The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  5  1 15 10  1  1  1  1  1  1  1  1  1  1  1 20  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1 15  1 15  1  1 10  1  1 15  1  5  1  1  1  1  1  1  1  0 20  1  1  1  1 20  1  1  1 10
 0  1  0 15 10  5  1 22  8 16 11 21 14  7  1 12  1  1 18 11  9  3  4 17 13  0 24  2 13  1  6 23 17 10 12  8 24 10  4 20  1 16 19  1 19  2  3 17 20 10 18  1  5 24  1  3 14  1 11  1  8  9 22  0  2 22  6 15  1  8  4 21 16  1 15 21 20  1
 0  0  1 16  7 24  4 14 19 22  8  5 12 17 23 15  2  9 23  6 20 10 21 18 11  3  4  6  7 16 17 21 19 12 16  2 10 11 18  5 24 23  2  6 21 22 20 13 24  1  0 13 15  9  7  4 11  8 24  0  3  9  7  6  8 19 12  1 10 13 20 23 10  7 18 16 12 15

generates a code of length 78 over Z25 who´s minimum homogenous weight is 302.

Homogenous weight enumerator: w(x)=1x^0+1380x^302+1420x^303+380x^304+8x^305+2160x^307+1580x^308+400x^309+48x^310+1640x^312+1200x^313+380x^314+56x^315+1360x^317+780x^318+180x^319+820x^322+620x^323+100x^324+640x^327+400x^328+60x^329+4x^330+8x^340

The gray image is a code over GF(5) with n=390, k=6 and d=302.
This code was found by Heurico 1.16 in 1.73 seconds.