The generator matrix

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

generates a code of length 13 over Z5[X]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+136x^35+100x^36+412x^40+800x^41+1000x^44+1580x^45+2000x^46+5000x^48+8000x^49+5404x^50+3200x^51+20000x^53+16000x^54+7320x^55+6400x^56+564x^60+208x^65

The gray image is a linear code over GF(5) with n=65, k=7 and d=35.
This code was found by Heurico 1.16 in 1.14 seconds.