The generator matrix

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

generates a code of length 7 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+10x^4+5x^6+32x^7+5x^8+10x^10+1x^14

The gray image is a linear code over GF(2) with n=14, k=6 and d=4.
This code was found by Heurico 1.16 in 0.000119 seconds.