The generator matrix

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

generates a code of length 3 over Z5[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+60x^4+12x^5+1200x^8+480x^9+48x^10+8000x^12+4800x^13+960x^14+64x^15

The gray image is a linear code over GF(5) with n=15, k=6 and d=4.
This code was found by Heurico 1.16 in 0.00186 seconds.