The generator matrix

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

generates a code of length 12 over Z5[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+192x^40+780x^41+360x^42+300x^44+1492x^45+2340x^46+480x^47+1500x^48+1200x^49+2916x^50+3380x^51+660x^52+12x^55+12x^60

The gray image is a linear code over GF(5) with n=60, k=6 and d=40.
This code was found by Heurico 1.16 in 0.0438 seconds.