The generator matrix

 1  1  1  1  1
 0  X  0  0  X
 0  0  X  0 3X
 0  0  0  X 3X

generates a code of length 5 over Z5[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+40x^10+120x^15+2760x^20+204x^25

The gray image is a linear code over GF(5) with n=25, k=5 and d=10.
This code was found by Heurico 1.16 in 0.000647 seconds.