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

generates a code of length 13 over Z5[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+152x^45+100x^46+300x^48+400x^50+200x^51+1200x^53+540x^55+200x^56+24x^60+8x^65

The gray image is a linear code over GF(5) with n=65, k=5 and d=45.
This code was found by Heurico 1.16 in 0.0031 seconds.