The generator matrix

 1  1  1  1  1  1  1  1
 0  X  0  0  0  0  X  0
 0  0  X  0  0  0 3X  0
 0  0  0  X  0  0 3X  0
 0  0  0  0  X  0 3X  0
 0  0  0  0  0  X 3X  0

generates a code of length 8 over Z5[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+60x^10+264x^15+960x^20+2264x^25+3880x^30+62500x^32+4920x^35+3276x^40

The gray image is a linear code over GF(5) with n=40, k=7 and d=10.
This code was found by Heurico 1.16 in 0.369 seconds.