The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+104x^17+222x^18+316x^19+507x^20+564x^21+626x^22+696x^23+475x^24+272x^25+170x^26+76x^27+41x^28+20x^29+6x^30

The gray image is a linear code over GF(2) with n=88, k=12 and d=34.
This code was found by Heurico 1.16 in 60.2 seconds.