The generator matrix

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

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+72x^14+138x^15+269x^16+508x^17+462x^18+1760x^19+720x^20+3728x^21+980x^22+3724x^23+822x^24+1808x^25+464x^26+512x^27+232x^28+96x^29+68x^30+10x^31+4x^32+4x^33+2x^34

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 3.26 seconds.