The generator matrix

 1  1  1  1  1
 0  X  0  0  0
 0  0  X  0  0
 0  0  0  X  0
 0  0  0  0  X

generates a code of length 5 over Z5[X]/(X^2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+20x^5+160x^10+640x^15+13780x^20+1024x^25

The gray image is a linear code over GF(5) with n=25, k=6 and d=5.
This code was found by Heurico 1.16 in 0.00851 seconds.