The generator matrix

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

generates a code of length 7 over Z5[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+20x^20+44x^25+500x^28+20x^30+40x^35

The gray image is a linear code over GF(5) with n=35, k=4 and d=20.
This code was found by Heurico 1.16 in 0.000168 seconds.