The generator matrix

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

generates a code of length 16 over Z25 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+144x^55+100x^56+176x^60+800x^61+96x^65+1600x^66+96x^70+80x^75+32x^80

The gray image is a code over GF(5) with n=80, k=5 and d=55.
This code was found by Heurico 1.16 in 0.00795 seconds.