The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+20x^5+100x^8+160x^10+1200x^13+640x^15+5000x^16+4800x^18+38780x^20+20000x^21+6400x^23+1024x^25

The gray image is a code over GF(5) with n=25, k=7 and d=5.
This code was found by Heurico 1.16 in 0.101 seconds.