The generator matrix

 1  0  0  1  1  1  1
 0  1  0  X  1  0  X
 0  0  1  1 X^2+X+1 X+1  1
 0  0  0 X^2  0 X^2 X^2
 0  0  0  0 X^2 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+90x^4+96x^5+549x^6+576x^7+549x^8+96x^9+90x^10+1x^14

The gray image is a linear code over GF(2) with n=28, k=11 and d=8.
As d=8 is an upper bound for linear (28,11,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 11.
This code was found by Heurico 1.16 in 0.00253 seconds.