The generator matrix

 1  0  1  1  1  0  1  1  1  1  1
 0  1  1  0  1  1  0  X  0  0  X
 0  0  X  0  0  X  X  X  0  0  0
 0  0  0  X  0  X  X  0  0  X  X
 0  0  0  0  X  X  X  X  X  X  0

generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+17x^8+16x^9+15x^10+32x^11+14x^12+16x^13+14x^14+3x^18

The gray image is a linear code over GF(2) with n=22, k=7 and d=8.
As d=8 is an upper bound for linear (22,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.000583 seconds.