The generator matrix

 1  0  1  1  1  1
 0  1 X+1 X^2+X X^3+X^2  0
 0  0 X^3  0 X^3 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+14x^4+104x^5+274x^6+104x^7+13x^8+2x^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 -6.48e-008 seconds.