The generator matrix

 1  0  1
 0  1 16
 0  0 15

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

Homogenous weight enumerator: w(x)=1x^0+12x^5+300x^8+48x^10+1500x^12+1200x^13+64x^15

The gray image is a code over GF(5) with n=15, k=5 and d=5.
This code was found by Heurico 1.16 in 0.00019 seconds.