The generator matrix

 1  1  1  1  1  1  1  1  1  5  1  1  1  1  1  1
 0  5  0  0  0  5  0  5  5  5  5 15 10 10  0  0
 0  0  5  0  0 15 10 20 15 10 20  0  0  5 10  0
 0  0  0  5  0 15 20 20 20 15  0  0 20 20  5  0
 0  0  0  0  5 15 15 10  5  5 15 10  5 20 20  0

generates a code of length 16 over Z25 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+96x^45+244x^50+396x^55+2980x^60+10720x^65+704x^70+380x^75+104x^80

The gray image is a code over GF(5) with n=80, k=6 and d=45.
This code was found by Heurico 1.16 in 0.147 seconds.