The generator matrix

 1  0  1  1  1 X^3
 0  1 X+1 X^3+X^2+X X+1  1
 0  0 X^2  0 X^2 X^3
 0  0  0 X^3+X^2 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+16x^3+151x^4+752x^5+2256x^6+752x^7+151x^8+16x^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.