The generator matrix

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

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+16x^20+60x^21+400x^24+36x^25+180x^26+500x^28+1600x^29+48x^30+260x^31+24x^35

The gray image is a linear code over GF(5) with n=35, k=5 and d=20.
This code was found by Heurico 1.16 in 0.00109 seconds.