The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+147x^20+136x^21+198x^22+156x^23+172x^24+52x^25+72x^26+36x^27+39x^28+4x^29+10x^30+1x^32

The gray image is a linear code over GF(2) with n=92, k=10 and d=40.
This code was found by Heurico 1.16 in 0.0254 seconds.