The generator matrix

 1  1  1  1  1  X  1
 0  X  0  0  0 X^2  X
 0  0  X  0  X X^2 X^2
 0  0  0  X  X X^2+X X^2+X
 0  0  0  0 X^2  0 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+77x^4+296x^6+256x^7+331x^8+56x^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 0.00617 seconds.