The generator matrix

 1  0  0  1  1  1 X^2
 0  1  0  1  X X^2+X  1
 0  0  1  1  1 X^2+1  X
 0  0  0  X  0 X^2+X 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+60x^4+192x^5+440x^6+648x^7+473x^8+176x^9+48x^10+8x^11+2x^12

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 0.00282 seconds.