The generator matrix

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

generates a code of length 8 over Z5[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+24x^15+20x^16+160x^20+320x^21+464x^25+1920x^26+10000x^28+880x^30+5120x^31+12500x^32+40000x^33+1080x^35+5120x^36+516x^40

The gray image is a linear code over GF(5) with n=40, k=7 and d=15.
This code was found by Heurico 1.16 in 0.238 seconds.