The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  X X^2  0  X  X  X  1  X  0  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0 X^2 X^2+X  X  0 X^2+X  0  X  X  X  0  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  0 X^2+X X^2  X X^2  X  X X^2  0  0  0
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X  0  X  X X^2+X  0  0 X^2+X X^2  0  0 X^2  0
 0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  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+56x^16+84x^17+145x^18+240x^19+327x^20+416x^21+505x^22+540x^23+487x^24+468x^25+331x^26+232x^27+137x^28+56x^29+43x^30+12x^31+12x^32+4x^36

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 0.241 seconds.