The generator matrix

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

generates a code of length 13 over Z5[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+200x^49+64x^50+300x^54+60x^55

The gray image is a linear code over GF(5) with n=65, k=4 and d=49.
This code was found by Heurico 1.16 in 0.000341 seconds.