The generator matrix

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

generates a code of length 20 over Z5[X]/(X^2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+36x^75+560x^80+20x^85+8x^100

The gray image is a linear code over GF(5) with n=100, k=4 and d=75.
This code was found by Heurico 1.16 in 0.0012 seconds.