The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+14x^22+2x^23+3x^24+4x^25+6x^26+2x^27

The gray image is a linear code over GF(2) with n=92, k=5 and d=44.
This code was found by Heurico 1.16 in 0.00241 seconds.