The generator matrix

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

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+56x^40+80x^41+200x^44+408x^45+360x^46+1000x^48+1600x^49+1092x^50+1040x^51+4000x^53+3200x^54+1388x^55+1020x^56+148x^60+32x^65

The gray image is a linear code over GF(5) with n=65, k=6 and d=40.
This code was found by Heurico 1.16 in 0.0587 seconds.