The generator matrix

 1  0  0  1  1  1
 0  1  0 3X+1  2  4
 0  0  1 3X+3  2  1

generates a code of length 6 over Z5[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+300x^16+660x^20+2400x^21+5000x^24+2424x^25+4800x^26+40x^30

The gray image is a linear code over GF(5) with n=30, k=6 and d=16.
This code was found by Heurico 1.16 in 0.00956 seconds.