The generator matrix

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

generates a code of length 10 over Z5[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+200x^37+120x^40+300x^42+4x^50

The gray image is a linear code over GF(5) with n=50, k=4 and d=37.
This code was found by Heurico 1.16 in 0.000223 seconds.