The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  1  1  X  X  1  1  X  1
 0  X  0  X  0  0  X X^2+X X^2 X^2  0 X^2  X  X X^2+X  X X^2+X X^2 X^2+X X^2  0 X^2  0
 0  0  X  X  0 X^2+X  X X^2  0  X  0  X X^2+X X^2  0 X^2+X  0  X X^2 X^2 X^2  X  0
 0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2 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+30x^18+58x^19+74x^20+126x^21+159x^22+156x^23+155x^24+116x^25+57x^26+42x^27+21x^28+14x^29+9x^30+4x^32+1x^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 0.0231 seconds.