The generator matrix
1 0 1 1
0 1 1 0
0 0 3X 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+100x^8+96x^10+1000x^12+800x^13+256x^15+7500x^16+4000x^17+1600x^18+256x^20
The gray image is a linear code over GF(5) with n=20, k=6 and d=5.
This code was found by Heurico 1.16 in 0.00407 seconds.