The generator matrix
1 1 1 1
0 X 0 0
0 0 X 0
0 0 0 X
generates a code of length 4 over Z5[X]/(X^2) who´s minimum homogenous weight is 5.
Homogenous weight enumerator: w(x)=1x^0+16x^5+96x^10+256x^15+2500x^16+256x^20
The gray image is a linear code over GF(5) with n=20, k=5 and d=5.
This code was found by Heurico 1.16 in 0.000383 seconds.