The generator matrix

 1  0  0  1  1  1  X  1  1  1  1 X^2 X^2+X X^2+X  1  1  1  1  0 X^2  X  1  1
 0  1  0  1 X^2+X X^2+X+1  1 X^2 X+1 X^2+1  X  1  0  1 X^2+1 X^2+X+1  X X^2+X  1  1 X^2  1  0
 0  0  1  1 X^2+X+1 X^2+X  1  X X+1  0  1  X  1 X+1 X+1  1  X  0 X+1  1 X^2 X^2+1  0
 0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  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+28x^16+96x^17+205x^18+324x^19+726x^20+648x^21+1640x^22+924x^23+1512x^24+688x^25+810x^26+284x^27+152x^28+104x^29+32x^30+4x^31+11x^32+1x^34+2x^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 0.563 seconds.