The generator matrix

 1  0  0  0  0  0  0  0  1  1  1  1  1  0  X  1  1  X  1  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  1  X X+1  X  1 X+1  1  X
 0  0  1  0  0  0  0  0  0  1  X  0  X  1  1  1 X+1  0  0  X  0  0
 0  0  0  1  0  0  0  0  1  0  X X+1  0  1  X X+1  1  1  X  1  0  0
 0  0  0  0  1  0  0  0  1  1 X+1  X  X  X X+1  1  0  0  1 X+1  X  0
 0  0  0  0  0  1  0  0  1  X  1  0 X+1  X  X  0 X+1 X+1  X  X  X  0
 0  0  0  0  0  0  1  0  1 X+1  0  X X+1  0 X+1  1  X X+1  0  1  X  0
 0  0  0  0  0  0  0  1  X  1  1  1 X+1 X+1  0  X X+1  X  0  0 X+1  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+104x^12+176x^13+607x^14+728x^15+1702x^16+2402x^17+3747x^18+5088x^19+6424x^20+8040x^21+7624x^22+7856x^23+6312x^24+5212x^25+3870x^26+2336x^27+1728x^28+792x^29+519x^30+120x^31+113x^32+18x^33+15x^34+2x^38

The gray image is a linear code over GF(2) with n=44, k=16 and d=12.
This code was found by Heurico 1.11 in 26 seconds.