The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  5  0  5
 0  1  1  7 14  0 16  7  5 14 19 16 12 15  1  1
 0  0 15 10  5  5 10 20 15 20  0 20  5 15  5 10

generates a code of length 16 over Z25 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+600x^58+160x^60+800x^63+436x^65+1100x^68+12x^70+12x^75+4x^80

The gray image is a code over GF(5) with n=80, k=5 and d=58.
This code was found by Heurico 1.16 in 3.2 seconds.