The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  1  1  0  X  1  1
 0  1  0  1  0  1  1  0  X  1 X+1  1  1  0  X X+1  0  1  1  1 X+1  1
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  1 X+1  X  0 X+1  X  1  X  1
 0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  X  0  0  X  0  X  X
 0  0  0  0  X  0  0  0  X  0  0  X  X  X  0  X  X  0  0  X  X  X
 0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  X  0  0  0  X  0
 0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  X  X  0  X  X  X  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+41x^16+167x^18+203x^20+218x^22+204x^24+120x^26+60x^28+6x^30+2x^32+1x^34+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 0.0291 seconds.