The generator matrix

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

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+632x^40+3520x^41+1600x^42+3400x^44+7376x^45+15840x^46+3200x^47+14500x^48+27200x^49+28920x^50+45760x^51+36300x^52+58000x^53+54400x^54+38536x^55+44880x^56+6400x^57+116x^60+44x^65

The gray image is a linear code over GF(5) with n=65, k=8 and d=40.
This code was found by Heurico 1.16 in 22.8 seconds.