The generator matrix

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

generates a code of length 10 over Z5[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+116x^20+432x^25+1240x^30+3280x^35+67240x^40+4104x^45+1712x^50

The gray image is a linear code over GF(5) with n=50, k=7 and d=20.
This code was found by Heurico 1.16 in 0.725 seconds.