The generator matrix

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

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+77x^16+96x^18+249x^20+192x^22+234x^24+96x^26+70x^28+8x^32+1x^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 0.0325 seconds.