The generator matrix

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

generates a code of length 6 over Z2[X]/(X^4) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+18x^2+63x^4+320x^5+1244x^6+320x^7+63x^8+18x^10+1x^12

The gray image is a linear code over GF(2) with n=48, k=11 and d=8.
This code was found by Heurico 1.16 in -3.24e-008 seconds.