The generator matrix

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

generates a code of length 13 over Z5[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+284x^40+380x^41+200x^42+700x^44+3024x^45+1860x^46+400x^47+1500x^48+5600x^49+11668x^50+5140x^51+8600x^52+6000x^53+11200x^54+15484x^55+5120x^56+800x^57+124x^60+40x^65

The gray image is a linear code over GF(5) with n=65, k=7 and d=40.
This code was found by Heurico 1.16 in 1.17 seconds.