The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  X  1  X  X  0  X  0  1  1  X  X
 0  X  0  0  0  X X^2+X  X  0  0 X^2  X X^2+X X^2 X^2+X  X X^2+X  X X^2  0 X^2  0
 0  0  X  0  X  X X^2+X  0  0 X^2 X^2+X  0 X^2+X  X  X X^2+X  0  X  0  X  X  0
 0  0  0  X  X  0 X^2+X  X  X X^2  X X^2+X X^2+X X^2  X  X  0  X X^2+X X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  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 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 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+139x^14+8x^15+464x^16+120x^17+1191x^18+616x^19+2586x^20+1304x^21+3462x^22+1304x^23+2676x^24+616x^25+1238x^26+120x^27+388x^28+8x^29+111x^30+27x^32+3x^34+2x^36

The gray image is a linear code over GF(2) with n=88, k=14 and d=28.
This code was found by Heurico 1.16 in 11.5 seconds.