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.