The generator matrix

 1  1  1  1  1  1  1  1
 0  X  0  0  X  X  0  X
 0  0  X  0 3X 2X  X 3X
 0  0  0  X 3X  X 4X 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+68x^20+72x^25+148x^30+2500x^32+208x^35+128x^40

The gray image is a linear code over GF(5) with n=40, k=5 and d=20.
This code was found by Heurico 1.16 in 0.0018 seconds.