The generator matrix

 1  0  0  1
 0  1  0 16
 0  0  1  8
 0  0  0 15

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

Homogenous weight enumerator: w(x)=1x^0+16x^5+600x^8+96x^10+6000x^12+4800x^13+256x^15+32500x^16+24000x^17+9600x^18+256x^20

The gray image is a code over GF(5) with n=20, k=7 and d=5.
This code was found by Heurico 1.16 in 0.0839 seconds.