The generator matrix

 1  0  1  1  1
 0  1 3X+1  2 3X+4

generates a code of length 5 over Z5[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+100x^16+120x^20+400x^21+4x^25

The gray image is a linear code over GF(5) with n=25, k=4 and d=16.
This code was found by Heurico 1.16 in 6.72e-005 seconds.