The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+158x^16+32x^18+180x^20+192x^22+336x^24+32x^26+72x^28+17x^32+4x^36

The gray image is a linear code over GF(2) with n=44, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0403 seconds.