The generator matrix

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

generates a code of length 28 over Z5[X]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+76x^100+176x^105+144x^110+2500x^112+44x^115+72x^120+60x^125+36x^130+8x^135+8x^140

The gray image is a linear code over GF(5) with n=140, k=5 and d=100.
This code was found by Heurico 1.16 in 0.0184 seconds.