The generator matrix

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

generates a code of length 10 over Z5[X]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+44x^35+548x^40+12x^45+20x^50

The gray image is a linear code over GF(5) with n=50, k=4 and d=35.
This code was found by Heurico 1.16 in 0.000344 seconds.