The generator matrix

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

generates a code of length 6 over Z5[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+60x^10+240x^15+780x^20+12500x^24+1224x^25+820x^30

The gray image is a linear code over GF(5) with n=30, k=6 and d=10.
This code was found by Heurico 1.16 in 0.0146 seconds.