The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  0 X^2  0  1  1  X  1  1  1  1  1
 0  X  0  X  0  0  X X^2+X  0  X X^2+X  X  X X^2  0  0 X^2  X  X  0  0  0
 0  0  X  X  0 X^2+X  X  0  X  X  0 X^2  X  X X^2+X  0  X  X  X X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+43x^12+116x^14+48x^15+278x^16+336x^17+744x^18+1008x^19+1719x^20+2704x^21+2376x^22+2704x^23+1736x^24+1008x^25+752x^26+336x^27+281x^28+48x^29+100x^30+33x^32+8x^34+5x^36

The gray image is a linear code over GF(2) with n=88, k=14 and d=24.
This code was found by Heurico 1.16 in 1.89 seconds.