The generator matrix

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

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+100x^16+160x^20+800x^21+424x^25+1600x^26+40x^30

The gray image is a linear code over GF(5) with n=30, k=5 and d=16.
This code was found by Heurico 1.16 in 0.000615 seconds.