The generator matrix

 1  0  1  1  1  0  1  1  0  1 X^2  1  1  X  0  1  1  1 X^2 X^2+X X^2  1  1
 0  1  1  0  1  1  0 X+1  1 X^2  1 X+1 X^2  0  1 X^2+X+1 X^2+X X^2+X+1  X  1  X X^2  0
 0  0  X  0  0  0  0  0  0 X^2 X^2  X X^2+X X^2 X^2+X  X  X  X X^2 X^2+X  0 X^2+X  0
 0  0  0  X  0  0 X^2+X X^2 X^2+X  0  X  X  X X^2+X  X X^2+X  X X^2 X^2+X X^2+X  0  0  0
 0  0  0  0  X X^2+X X^2+X X^2  X  X  0 X^2  X  X  0 X^2+X X^2 X^2+X  0  0  X  0  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 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+33x^16+110x^17+238x^18+316x^19+796x^20+674x^21+1512x^22+880x^23+1474x^24+658x^25+777x^26+332x^27+252x^28+94x^29+32x^30+8x^31+4x^32+1x^42

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 0.796 seconds.