The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  0  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  X  0  X  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  0  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  0  0  X  X  X  0  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  X  0  X  0
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  0  X  0

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+66x^10+186x^12+309x^14+583x^16+984x^18+3320x^20+5479x^22+3327x^24+970x^26+610x^28+323x^30+152x^32+60x^34+12x^36+1x^38+1x^40

The gray image is a linear code over GF(2) with n=44, k=14 and d=10.
This code was found by Heurico 1.16 in 7.76 seconds.