The generator matrix

 1  0  1  1  1  0  1  1  X  1  1
 0  1  1  0  1  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  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+32x^6+190x^8+232x^10+316x^12+112x^14+89x^16+8x^18+8x^20

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 0.00336 seconds.