The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+50x^18+16x^19+105x^20+64x^21+236x^22+96x^23+236x^24+64x^25+84x^26+16x^27+38x^28+12x^30+3x^32+2x^34+1x^36

The gray image is a linear code over GF(2) with n=92, k=10 and d=36.
This code was found by Heurico 1.16 in 0.376 seconds.