The generator matrix

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

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+84x^10+420x^15+1820x^20+4284x^25+62500x^28+5740x^30+3276x^35

The gray image is a linear code over GF(5) with n=35, k=7 and d=10.
This code was found by Heurico 1.16 in 0.369 seconds.