The generator matrix

 1  0  1  1  1  0  1  1  X  1  1 X^2+X  X  X  0 X^2  X X^2 X^2+X  1  1  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+X X^2+1  1 X^2  X  1  1  1  X  1  0 X^2+X+1  0
 0  0  X X^2+X  0 X^2+X  X X^2+X  X X^2  0  0  X  X  0  X  X  X  0  0  X  0
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  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+43x^14+62x^15+177x^16+276x^17+671x^18+1236x^19+1869x^20+2516x^21+2654x^22+2528x^23+1878x^24+1244x^25+702x^26+268x^27+162x^28+60x^29+23x^30+2x^31+8x^32+3x^34+1x^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 2.2 seconds.