The generator matrix

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

generates a code of length 14 over Z5[X]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+148x^35+696x^40+1224x^45+2384x^50+4260x^55+62500x^56+3912x^60+2264x^65+736x^70

The gray image is a linear code over GF(5) with n=70, k=7 and d=35.
This code was found by Heurico 1.16 in 2.23 seconds.