The generator matrix

 1  1
 0 3X+1

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

Homogenous weight enumerator: w(x)=1x^0+40x^4+8x^5+400x^8+160x^9+16x^10

The gray image is a linear code over GF(5) with n=10, k=4 and d=4.
This code was found by Heurico 1.16 in 1.69e-005 seconds.