The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+104x^14+478x^16+893x^18+1624x^20+1973x^22+1608x^24+1026x^26+360x^28+98x^30+25x^32+1x^34+1x^38

The gray image is a linear code over GF(2) with n=44, k=13 and d=14.
This code was found by Heurico 1.16 in 1.42 seconds.