The generator matrix

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

generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+22x^6+16x^7+23x^8+2x^10

The gray image is a linear code over GF(2) with n=28, k=6 and d=12.
As d=12 is an upper bound for linear (28,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 9.01e-005 seconds.