The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+36x^15+106x^16+136x^18+336x^19+192x^20+128x^22+504x^23+200x^24+240x^26+144x^27+4x^31+13x^32+8x^34

The gray image is a linear code over GF(2) with n=44, k=11 and d=15.
This code was found by Heurico 1.16 in 7.68 seconds.