The generator matrix

 1  1  1
 0  X  0
 0  0  X

generates a code of length 3 over Z5[X]/(X^2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+12x^5+48x^10+500x^12+64x^15

The gray image is a linear code over GF(5) with n=15, k=4 and d=5.
This code was found by Heurico 1.16 in 3.6e-005 seconds.