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

generates a code of length 72 over Z25 who´s minimum homogenous weight is 278.

Homogenous weight enumerator: w(x)=1x^0+1620x^278+1140x^279+164x^280+2800x^283+1120x^284+164x^285+2020x^288+1180x^289+120x^290+1620x^293+880x^294+100x^295+1400x^298+520x^299+44x^300+540x^303+160x^304+16x^305+16x^310

The gray image is a code over GF(5) with n=360, k=6 and d=278.
This code was found by Heurico 1.16 in 1.9 seconds.