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.