The generator matrix

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

generates a code of length 78 over Z25 who´s minimum homogenous weight is 311.

Homogenous weight enumerator: w(x)=1x^0+160x^311+400x^312+8x^315+40x^316+8x^320+8x^340

The gray image is a code over GF(5) with n=390, k=4 and d=311.
This code was found by Heurico 1.16 in 0.063 seconds.