The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0  1  1  0  0  0  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1  1  1  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  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 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  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+28x^12+108x^14+314x^16+256x^17+552x^18+1280x^19+1708x^20+2560x^21+2728x^22+2560x^23+1704x^24+1280x^25+672x^26+256x^27+308x^28+12x^30+29x^32+24x^34+4x^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 1.25 seconds.