The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+72x^14+331x^16+728x^18+128x^19+1801x^20+1024x^21+3140x^22+1792x^23+3222x^24+1024x^25+1956x^26+128x^27+710x^28+228x^30+78x^32+20x^34+1x^36

The gray image is a linear code over GF(2) with n=92, k=14 and d=28.
This code was found by Heurico 1.16 in 3.07 seconds.