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

generates a code of length 69 over Z25 who´s minimum homogenous weight is 275.

Homogenous weight enumerator: w(x)=1x^0+492x^275+120x^280+12x^300

The gray image is a code over GF(5) with n=345, k=4 and d=275.
This code was found by Heurico 1.16 in 3.14 seconds.