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.