The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^4+16x^5+2400x^8+960x^9+96x^10+32000x^12+19200x^13+3840x^14+256x^15+160000x^16+128000x^17+38400x^18+5120x^19+256x^20

The gray image is a linear code over GF(5) with n=20, k=8 and d=4.
This code was found by Heurico 1.16 in 1.08 seconds.