The generator matrix

 1  0  0  0  1  1  1 15  1  1  1  1  5  5  1  1
 0  1  0  0 15  1 16  1  5  6 22  5  1  1 16 12
 0  0  1  0 16  1 22 16 20 10 19 21 18 13 12  6
 0  0  0  1  8  5 13 13  7 18  2 17 10  9  5  6

generates a code of length 16 over Z25 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+824x^50+1160x^52+2080x^53+2440x^54+3496x^55+3400x^56+9720x^57+11160x^58+6680x^59+16236x^60+27200x^61+43080x^62+29440x^63+26820x^64+44576x^65+54400x^66+56040x^67+29820x^68+11560x^69+10416x^70+56x^75+20x^80

The gray image is a code over GF(5) with n=80, k=8 and d=50.
This code was found by Heurico 1.16 in 37.2 seconds.