The generator matrix

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

generates a code of length 13 over Z5[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+120x^44+976x^45+480x^46+200x^48+960x^49+2944x^50+640x^51+1500x^52+800x^53+1920x^54+4184x^55+880x^56+8x^60+12x^65

The gray image is a linear code over GF(5) with n=65, k=6 and d=44.
This code was found by Heurico 1.16 in 0.0502 seconds.