The generator matrix

 1  1  1  1
 0  5  0  0
 0  0  5  0
 0  0  0  5

generates a code of length 4 over Z25 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+16x^5+96x^10+256x^15+2500x^16+256x^20

The gray image is a code over GF(5) with n=20, k=5 and d=5.
This code was found by Heurico 1.16 in 0.000386 seconds.