The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  X  0  1  1  1  X  1  0  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  X  1  1 X+1  X  1  1  1  0  0
 0  0  1  0  0  0  1  1  1  1  1  0  0  1  0  X  1  1 X+1  X  1  0
 0  0  0  1  0  1  1  0  1  0  1  1  1  1 X+1  0  1  1  1  X  1  0
 0  0  0  0  1  1  0  1  1  0  1 X+1 X+1  0  0  1 X+1  1  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  X  X  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  0  X  X  0  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  X  0  X  X  X  0
 0  0  0  0  0  0  0  0  0  X  X  0  0  X  0  0  X  X  0  X  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+74x^12+138x^13+304x^14+510x^15+776x^16+1376x^17+1882x^18+2704x^19+3242x^20+3476x^21+3816x^22+3420x^23+3244x^24+2720x^25+1900x^26+1440x^27+790x^28+466x^29+280x^30+118x^31+59x^32+16x^33+10x^34+6x^36

The gray image is a linear code over GF(2) with n=44, k=15 and d=12.
This code was found by Heurico 1.16 in 12.4 seconds.