The generator matrix

 1  0  0  0  1  1  1  1  1  1  1
 0  1  0  0  1  0  0  1 X+1  0  0
 0  0  1  0  1  0  1  0  1  0  0
 0  0  0  1  1  1  0  0  1  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  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+76x^4+224x^6+782x^8+944x^10+1028x^12+704x^14+281x^16+48x^18+8x^20

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 0.0273 seconds.