The generator matrix

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

generates a code of length 28 over Z5[X]/(X^2) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+240x^106+800x^107+64x^110+320x^111+400x^112+48x^115+440x^116+800x^117+12x^120

The gray image is a linear code over GF(5) with n=140, k=5 and d=106.
This code was found by Heurico 1.16 in 0.00906 seconds.