The generator matrix

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

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+40x^2+48x^3+135x^4+656x^5+2336x^6+656x^7+135x^8+48x^9+40x^10+1x^12

The gray image is a linear code over GF(2) with n=48, k=12 and d=8.
This code was found by Heurico 1.16 in 1.05e-007 seconds.