The generator matrix

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

generates a code of length 4 over Z5[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+24x^10+48x^15+500x^16+52x^20

The gray image is a linear code over GF(5) with n=20, k=4 and d=10.
This code was found by Heurico 1.16 in 6.01e-005 seconds.