The generator matrix

 1  0  0  1  1  1  X  1  1  1  1
 0  1  0  X  1 X+1  1  X  0  0  1
 0  0  1  1 X+1  X  1 X+1  1  X  1

generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+12x^9+18x^10+12x^11+6x^12+4x^13+6x^14+4x^15+1x^16

The gray image is a linear code over GF(2) with n=22, k=6 and d=9.
As d=9 is an upper bound for linear (22,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.000314 seconds.