The generator matrix

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

generates a code of length 8 over Z5[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+48x^20+352x^25+2500x^28+1128x^30+10000x^33+1488x^35+108x^40

The gray image is a linear code over GF(5) with n=40, k=6 and d=20.
This code was found by Heurico 1.16 in 0.0183 seconds.