The generator matrix

 1  1  1  1  1  1
 0 X^3+X^2  0 X^2  0  0
 0  0 X^3+X^2 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+16x^2+55x^4+880x^6+55x^8+16x^10+1x^12

The gray image is a linear code over GF(2) with n=48, k=10 and d=8.
This code was found by Heurico 1.16 in -3.24e-008 seconds.