The generator matrix

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

generates a code of length 5 over Z5[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+40x^15+500x^16+540x^20+2000x^21+44x^25

The gray image is a linear code over GF(5) with n=25, k=5 and d=15.
This code was found by Heurico 1.16 in 0.000501 seconds.