The generator matrix

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

generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+91x^2+1001x^4+5051x^6+4096x^7+5051x^8+1001x^10+91x^12+1x^14

The gray image is a linear code over GF(2) with n=28, k=14 and d=4.
This code was found by Heurico 1.16 in 0.11 seconds.