The generator matrix

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

generates a code of length 4 over Z5[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+120x^8+24x^10+1200x^12+960x^13+48x^15+6500x^16+4800x^17+1920x^18+52x^20

The gray image is a linear code over GF(5) with n=20, k=6 and d=8.
This code was found by Heurico 1.16 in 0.00372 seconds.