The generator matrix

 1  1  1  1  1  1  1
 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  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+10x^4+5x^6+96x^7+5x^8+10x^10+1x^14

The gray image is a linear code over GF(2) with n=28, k=7 and d=8.
This code was found by Heurico 1.16 in 0.000129 seconds.