The generator matrix

 1  1  1
 0  5  0
 0  0  5

generates a code of length 3 over Z25 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+12x^5+48x^10+500x^12+64x^15

The gray image is a code over GF(5) with n=15, k=4 and d=5.
This code was found by Heurico 1.16 in -6.87e-008 seconds.