The generator matrix

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

generates a code of length 7 over Z5[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+40x^10+140x^15+380x^20+724x^25+12500x^28+1020x^30+820x^35

The gray image is a linear code over GF(5) with n=35, k=6 and d=10.
This code was found by Heurico 1.16 in 0.0152 seconds.