The generator matrix

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

generates a code of length 6 over Z5[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+84x^20+40x^21+100x^24+336x^25+60x^26+4x^30

The gray image is a linear code over GF(5) with n=30, k=4 and d=20.
This code was found by Heurico 1.16 in 9.89e-005 seconds.