The generator matrix

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

generates a code of length 13 over Z5[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+200x^30+508x^35+1220x^40+1940x^45+3844x^50+62500x^52+3980x^55+2812x^60+1120x^65

The gray image is a linear code over GF(5) with n=65, k=7 and d=30.
This code was found by Heurico 1.16 in 1.68 seconds.