The generator matrix

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

generates a code of length 13 over Z5[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+24x^45+56x^50+500x^52+20x^55+8x^60+16x^65

The gray image is a linear code over GF(5) with n=65, k=4 and d=45.
This code was found by Heurico 1.16 in 0.000551 seconds.