The generator matrix

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

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+64x^40+156x^45+500x^48+100x^50+2000x^53+96x^55+176x^60+32x^65

The gray image is a linear code over GF(5) with n=65, k=5 and d=40.
This code was found by Heurico 1.16 in 0.00567 seconds.