The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  1  0  1  0  1  0  1  1  1
 0  1  1  0  1  1  0  1  1  X X+1  1  0  0 X+1  1 X+1  1 X+1  1  0  0  0
 0  0  X  0  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  X  X  X  X
 0  0  0  0  X  0  0  0  X  0  X  X  0  X  0  0  X  0  X  0  X  X  X
 0  0  0  0  0  X  0  0  X  0  0  0  X  X  0  X  X  X  X  X  X  X  X
 0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  0  0  0  X  X  0  X  X
 0  0  0  0  0  0  0  X  X  0  X  X  X  0  X  X  0  0  X  X  X  X  X

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+47x^16+56x^18+208x^20+184x^22+262x^24+136x^26+100x^28+8x^30+18x^32+4x^36

The gray image is a linear code over GF(2) with n=46, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0339 seconds.