The generator matrix

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

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+16x^4+8x^5+62x^6+80x^7+67x^8+8x^9+10x^10+4x^12

The gray image is a linear code over GF(2) with n=28, k=8 and d=8.
This code was found by Heurico 1.16 in 0.0002 seconds.