The generator matrix

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

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+56x^35+336x^40+440x^45+2500x^48+624x^50+10000x^53+960x^55+544x^60+164x^65

The gray image is a linear code over GF(5) with n=65, k=6 and d=35.
This code was found by Heurico 1.16 in 0.1 seconds.