The generator matrix

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

generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+36x^4+9x^6+126x^8+84x^10+512x^11+84x^12+126x^14+9x^16+36x^18+1x^22

The gray image is a linear code over GF(2) with n=22, k=10 and d=4.
This code was found by Heurico 1.16 in 0.00447 seconds.