The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+33x^14+44x^15+118x^16+194x^17+237x^18+326x^19+392x^20+426x^21+490x^22+502x^23+397x^24+358x^25+226x^26+146x^27+112x^28+46x^29+37x^30+6x^31+3x^32+1x^34+1x^40

The gray image is a linear code over GF(2) with n=44, k=12 and d=14.
This code was found by Heurico 1.16 in 0.351 seconds.