The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  X  X  X  1 X^2  X  1  X  0  1  1
 0  X  0  0  0  X X^2+X  X X^2  0  X X^2+X X^2+X  X X^2+X  0  0  X X^2 X^2  X  0
 0  0  X  0  X  X X^2+X  0  0  X X^2 X^2+X  0 X^2+X  0  X X^2+X  X X^2 X^2  0  0
 0  0  0  X  X  0 X^2+X  X  X  X X^2+X X^2+X  0  0 X^2 X^2+X X^2  X X^2+X  X  X  0
 0  0  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  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 14.

Homogenous weight enumerator: w(x)=1x^0+27x^14+92x^15+143x^16+230x^17+345x^18+566x^19+879x^20+1142x^21+1282x^22+1166x^23+922x^24+610x^25+358x^26+210x^27+94x^28+66x^29+35x^30+14x^31+6x^32+1x^34+3x^36

The gray image is a linear code over GF(2) with n=88, k=13 and d=28.
This code was found by Heurico 1.16 in 0.843 seconds.