The generator matrix

 1  1  1  X  1  X
 0  X  0  X X^3+X^2+X X^2+X
 0  0 X^3+X^2  0 X^2 X^2
 0  0  0 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+119x^4+368x^5+1040x^6+368x^7+119x^8+16x^9+1x^12

The gray image is a linear code over GF(2) with n=48, k=11 and d=12.
This code was found by Heurico 1.16 in 0.016 seconds.