The generator matrix

 1  1  1  1  1  1
 0  X  0  0  X  X
 0  0  X  0 3X 2X
 0  0  0  X 3X  X

generates a code of length 6 over Z5[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+80x^15+120x^20+2500x^24+264x^25+160x^30

The gray image is a linear code over GF(5) with n=30, k=5 and d=15.
This code was found by Heurico 1.16 in 0.000963 seconds.