The generator matrix

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

generates a code of length 14 over Z5[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+392x^50+200x^52+532x^55+500x^56+800x^57+676x^60+20x^65+4x^70

The gray image is a linear code over GF(5) with n=70, k=5 and d=50.
This code was found by Heurico 1.16 in 0.0194 seconds.