The generator matrix

 1  0  0  0  1  1  1  0  1  1  X  1  1  0  X  0  0  0  0  X  0  1
 0  1  0  0  0  1  1  1  0  0  0 X+1 X+1  1  1  1  1  1  1  X  1  0
 0  0  1  0  1  1  0  1  0  1  1  1  0  X  1  0  0  0  X  X  0  0
 0  0  0  1  1  0  1  1  1  0  1  1  X  1  0  0  0  0  1  1  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  0  X  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  X  X  0  0  X  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  0  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  0  0  X  X  0  0  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+50x^12+52x^13+155x^14+250x^15+387x^16+674x^17+969x^18+1336x^19+1605x^20+1792x^21+1846x^22+1756x^23+1610x^24+1356x^25+986x^26+696x^27+404x^28+220x^29+127x^30+58x^31+34x^32+2x^33+13x^34+5x^36

The gray image is a linear code over GF(2) with n=44, k=14 and d=12.
This code was found by Heurico 1.16 in 6.45 seconds.