The generator matrix

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

generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+6x^10+6x^12+2x^14+1x^16

The gray image is a linear code over GF(2) with n=22, k=4 and d=10.
This code was found by Heurico 1.16 in 0.000216 seconds.