The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+164x^16+8x^17+386x^18+144x^19+923x^20+504x^21+1595x^22+736x^23+1586x^24+504x^25+970x^26+144x^27+372x^28+8x^29+116x^30+25x^32+4x^34+1x^36+1x^38

The gray image is a linear code over GF(2) with n=92, k=13 and d=32.
This code was found by Heurico 1.16 in 1.05 seconds.