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

generates a code of length 79 over Z25 who´s minimum homogenous weight is 306.

Homogenous weight enumerator: w(x)=1x^0+1120x^306+1360x^307+1020x^308+12x^310+1800x^311+1580x^312+620x^313+48x^315+1400x^316+1260x^317+460x^318+52x^320+880x^321+820x^322+440x^323+740x^326+660x^327+360x^328+560x^331+320x^332+100x^333+12x^335

The gray image is a code over GF(5) with n=395, k=6 and d=306.
This code was found by Heurico 1.16 in 30.6 seconds.