The generator matrix

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

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+89x^12+84x^13+210x^14+448x^15+858x^16+1148x^17+1658x^18+2688x^19+3453x^20+3976x^21+3988x^22+3584x^23+3024x^24+2616x^25+2100x^26+1408x^27+707x^28+356x^29+218x^30+64x^31+53x^32+12x^33+18x^34+7x^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 11.1 seconds.