The generator matrix

 1  1  1  1  1  1  1  1
 0  X  0  0  0  X  0  X
 0  0  X  0  0 3X 2X 3X
 0  0  0  X  0 3X 4X 3X
 0  0  0  0  X 3X 3X 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+84x^15+160x^20+464x^25+780x^30+12500x^32+980x^35+656x^40

The gray image is a linear code over GF(5) with n=40, k=6 and d=15.
This code was found by Heurico 1.16 in 0.0217 seconds.