The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  0  X  1  1  1  1  0  X  1  1  1  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  X X^2+X X^2+X X^2+X  X  0  X X^2+X X^2+X  0  0  0
 0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2

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+47x^16+64x^18+250x^20+128x^21+392x^22+256x^23+463x^24+128x^25+176x^26+116x^28+8x^30+16x^32+2x^36+1x^40

The gray image is a linear code over GF(2) with n=92, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0677 seconds.