The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+40x^12+4x^13+176x^14+68x^15+242x^16+304x^17+272x^18+688x^19+656x^20+984x^21+1120x^22+984x^23+952x^24+688x^25+352x^26+304x^27+72x^28+68x^29+112x^30+4x^31+85x^32+16x^34

The gray image is a linear code over GF(2) with n=44, k=13 and d=12.
This code was found by Heurico 1.16 in 0.959 seconds.