The generator matrix

 1  1  1  1  1  1
 0  X  0  0  0  0
 0  0  X  0  0  0
 0  0  0  X  0  0
 0  0  0  0  X  0
 0  0  0  0  0  X

generates a code of length 6 over Z5[X]/(X^2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+24x^5+240x^10+1280x^15+3840x^20+62500x^24+6144x^25+4096x^30

The gray image is a linear code over GF(5) with n=30, k=7 and d=5.
This code was found by Heurico 1.16 in 0.212 seconds.