The generator matrix

 1  1  1  1  X  X  X
 0  X  0  X  0  X  0
 0  0  X  X  X  X  0

generates a code of length 7 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+6x^6+7x^8+2x^10

The gray image is a linear code over GF(2) with n=14, k=4 and d=6.
This code was found by Heurico 1.16 in 9.99e-005 seconds.