The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+124x^12+136x^14+1058x^16+1568x^18+3412x^20+3760x^22+3448x^24+1568x^26+1060x^28+136x^30+101x^32+12x^36

The gray image is a linear code over GF(2) with n=44, k=14 and d=12.
This code was found by Heurico 1.16 in 3.39 seconds.