The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X X^2
 0  X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2  X  0 X^2  0 X^2 X^2+X X^2+X X^2
 0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2
 0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0
 0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 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+28x^20+16x^21+75x^22+32x^23+60x^24+16x^25+18x^26+6x^28+3x^30+1x^40

The gray image is a linear code over GF(2) with n=92, k=8 and d=40.
This code was found by Heurico 1.16 in 0.00515 seconds.