The generator matrix

 1  0  0  1  1  1  0  1  1  X  1
 0  1  0  1  0  1  1  0  0  0  0
 0  0  1  1  1  0  1  0  0  0  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+60x^4+129x^6+128x^7+390x^8+512x^9+444x^10+768x^11+444x^12+512x^13+390x^14+128x^15+129x^16+60x^18+1x^22

The gray image is a linear code over GF(2) with n=22, k=12 and d=4.
This code was found by Heurico 1.16 in 0.029 seconds.