The generator matrix

 1  1  1  1  X  1  1
 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  0  0
 0  0  0  0  0 X^2  0
 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+31x^2+221x^4+1283x^6+1024x^7+1283x^8+221x^10+31x^12+1x^14

The gray image is a linear code over GF(2) with n=28, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00726 seconds.