The generator matrix

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

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+124x^20+80x^21+1200x^24+1328x^25+360x^26+2500x^28+9600x^29+4944x^30+1040x^31+20000x^32+10000x^33+19200x^34+6624x^35+1020x^36+104x^40

The gray image is a linear code over GF(5) with n=40, k=7 and d=20.
This code was found by Heurico 1.16 in 0.378 seconds.