The generator matrix

 1  0  1  1  1  0  1  1 X^2  1 X^2+X  1  0  1  1  1  X  X  0  X  1  1  1
 0  1  1  0 X+1  1 X+1  0  1  X  1 X^2+X+1  1 X^2+1 X^2  1 X^2+X  1  0  1  1 X^2+1  0
 0  0  X  0  0  0  X  X  X X^2+X X^2+X  0  X  X X^2 X^2+X  X X^2+X  X  X X^2+X  X  0
 0  0  0  X  0 X^2+X  X  X X^2 X^2  X  X X^2+X  X X^2+X  0  X  0  0 X^2 X^2 X^2+X  0
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  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+31x^16+78x^17+185x^18+414x^19+427x^20+1158x^21+894x^22+1806x^23+900x^24+1194x^25+428x^26+394x^27+164x^28+66x^29+26x^30+10x^31+12x^32+3x^34+1x^36

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 0.834 seconds.