The generator matrix

 1  1  1  1  1  1
 0  X  0  X X^3 X^3+X^2
 0  0  X  X  0  X
 0  0  0 X^2 X^3+X^2 X^3+X^2

generates a code of length 6 over Z2[X]/(X^4) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+48x^3+151x^4+464x^5+2768x^6+464x^7+151x^8+48x^9+1x^12

The gray image is a linear code over GF(2) with n=48, k=12 and d=12.
This code was found by Heurico 1.16 in 0.015 seconds.