The generator matrix

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

generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+45x^4+96x^5+200x^6+320x^7+235x^8+96x^9+24x^10+7x^12

The gray image is a linear code over GF(2) with n=28, k=10 and d=8.
This code was found by Heurico 1.16 in 0.000813 seconds.