The generator matrix

 1  0  0  0  0  1  1  1 X^2+X  1  1 X^2  0 X^2+X  1  1  1 X^2+X X^2  0  1  0  1
 0  1  0  0  0  0 X^2  0 X^2 X^2+1 X+1  1  X  1 X+1  0  1 X^2+X  1  X X^2+1  1  X
 0  0  1  0  0  0  1  1  1 X^2+1 X^2+X+1 X+1  1 X+1 X^2  X  0 X^2+X X^2+X  1 X^2+X+1  1  0
 0  0  0  1  0  1  1  X X^2+X+1 X^2 X^2 X^2+X  1  1  X  0  X  1 X^2+1 X^2 X^2+1  1  0
 0  0  0  0  1  1  X X+1 X+1  X X^2+1 X^2+X+1 X^2+X X^2+X+1 X^2+X  1  1 X^2+1 X^2+1  1 X^2+X X^2  1
 0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  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+115x^16+484x^17+1571x^18+2628x^19+5059x^20+6958x^21+10646x^22+10416x^23+10551x^24+7354x^25+5426x^26+2356x^27+1253x^28+498x^29+174x^30+24x^31+13x^32+2x^33+7x^34

The gray image is a linear code over GF(2) with n=92, k=16 and d=32.
This code was found by Heurico 1.13 in 11.2 seconds.