The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^4+404x^6+49x^8+4x^10

The gray image is a linear code over GF(2) with n=48, k=9 and d=16.
This code was found by Heurico 1.16 in 6.87e-008 seconds.