The generator matrix

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

generates a code of length 5 over Z25 who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+40x^15+540x^20+44x^25

The gray image is a code over GF(5) with n=25, k=4 and d=15.
This code was found by Heurico 1.16 in 3.24e-008 seconds.