The generator matrix

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

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+28x^2+10x^3+86x^4+120x^5+141x^6+1276x^7+141x^8+120x^9+86x^10+10x^11+28x^12+1x^14

The gray image is a linear code over GF(2) with n=28, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00174 seconds.