The generator matrix

 1  0  0  0  0  0  1  X  1  1  1
 0  1  0  0  0  0  0  1  X  0  0
 0  0  1  0  0  0  0  1 X+1  X  0
 0  0  0  1  0  0  1  0  1 X+1  0
 0  0  0  0  1  0  1  0  0  X  0
 0  0  0  0  0  1  1  0  X  1  0
 0  0  0  0  0  0  X  X  0  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+22x^4+112x^5+199x^6+336x^7+664x^8+976x^9+1162x^10+1248x^11+1162x^12+976x^13+664x^14+336x^15+199x^16+112x^17+22x^18+1x^22

The gray image is a linear code over GF(2) with n=22, k=13 and d=4.
This code was found by Heurico 1.16 in 0.133 seconds.