The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1
 0  X  0  0  0  0  0  0 X^2 X^2+X X^2+X  X X^2 X^2 X^2  X  X  0  X  0  X  0
 0  0  X  0  0  0  0 X^2 X^2+X  X X^2+X  0 X^2  0  X X^2  X X^2 X^2  X  X  0
 0  0  0  X  0  0  0 X^2+X X^2  X X^2+X X^2  0  X  X  X X^2+X X^2 X^2+X  X  0 X^2+X
 0  0  0  0  X  0  X  X X^2+X X^2+X  0 X^2+X X^2  X  0 X^2 X^2+X  0 X^2+X X^2 X^2+X X^2+X
 0  0  0  0  0  X  X X^2 X^2 X^2+X X^2+X  0  0  X X^2+X  X  0 X^2+X  0 X^2+X X^2+X  0
 0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 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+71x^14+124x^15+259x^16+332x^17+443x^18+574x^19+787x^20+3064x^21+5059x^22+3034x^23+797x^24+652x^25+480x^26+290x^27+201x^28+112x^29+90x^30+10x^31+3x^32+1x^42

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 3.36 seconds.