The generator matrix

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

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+36x^50+48x^55+500x^56+24x^60+16x^70

The gray image is a linear code over GF(5) with n=70, k=4 and d=50.
This code was found by Heurico 1.16 in 0.000626 seconds.