The generator matrix

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

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+616x^20+620x^21+3900x^24+5860x^25+3540x^26+29500x^28+31200x^29+24396x^30+9060x^31+60000x^32+118000x^33+62400x^34+32156x^35+9280x^36+96x^40

The gray image is a linear code over GF(5) with n=40, k=8 and d=20.
This code was found by Heurico 1.16 in 8.55 seconds.