The generator matrix

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

generates a code of length 6 over Z5[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+40x^12+80x^15+900x^16+480x^17+6120x^20+7200x^21+1920x^22+20000x^24+24264x^25+14400x^26+2560x^27+160x^30

The gray image is a linear code over GF(5) with n=30, k=7 and d=12.
This code was found by Heurico 1.16 in 0.143 seconds.