The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  0  X  1  1  0  1  X  0  1  X  1  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  X X^2 X^2+X  X X^2+X  0 X^2+X  X  0 X^2+X  X X^2  0  0  0
 0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 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  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2
 0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  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+103x^16+120x^18+642x^20+1128x^22+1311x^24+520x^26+220x^28+24x^30+24x^32+2x^36+1x^40

The gray image is a linear code over GF(2) with n=92, k=12 and d=32.
This code was found by Heurico 1.16 in 3.47 seconds.