The generator matrix

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

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+70x^16+44x^17+110x^18+188x^19+216x^20+484x^21+612x^22+628x^23+640x^24+468x^25+248x^26+196x^27+88x^28+28x^29+44x^30+12x^31+9x^32+10x^34

The gray image is a linear code over GF(2) with n=92, k=12 and d=32.
This code was found by Heurico 1.16 in 0.238 seconds.