The generator matrix

 1  0  0  0  0  1  1  1  1  1  1
 0  1  0  0  0  0  0  1  X  1  0
 0  0  1  0  0  0  1  1  0 X+1  1
 0  0  0  1  0  1  1  0  1  0 X+1
 0  0  0  0  1  1  0  0  X  1  X
 0  0  0  0  0  X  0  X  X  0  X
 0  0  0  0  0  0  X  X  X  X  0

generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+32x^5+83x^6+158x^7+317x^8+488x^9+611x^10+694x^11+643x^12+480x^13+321x^14+170x^15+62x^16+24x^17+9x^18+2x^19+1x^20

The gray image is a linear code over GF(2) with n=22, k=12 and d=5.
This code was found by Heurico 1.16 in 0.0414 seconds.