The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  1  1  1  0  1  1  0  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  X X+1 X+1  1  1  X X+1  1 X+1  1  0  0
 0  0  1  0  0  0  0  0  0  1 X+1 X+1  X X+1  X X+1  X  X  1 X+1  X  0
 0  0  0  1  0  0  0  1  1  1  1 X+1  1  X X+1  X  0  0  0  X X+1  0
 0  0  0  0  1  0  1  1  0  1  0  X  0  1  X X+1 X+1 X+1  X  0  1  0
 0  0  0  0  0  1  1  0  1 X+1  0  1  0  1  1  X  0  1  X  X  0  0
 0  0  0  0  0  0  X  0  0  X  X  0  X  0  X  0  X  0  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  0  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  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+56x^12+144x^13+312x^14+536x^15+873x^16+1304x^17+1792x^18+2696x^19+3038x^20+3512x^21+4240x^22+3512x^23+3038x^24+2696x^25+1792x^26+1304x^27+873x^28+536x^29+312x^30+144x^31+56x^32+1x^44

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 14.8 seconds.