The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  1  X  1  1  1  0  1  1  X
 0  1  0  0  0  1  1  1  X  0 X+1 X+1  1  1  1  X  1  X  X  0 X+1 X+1  X
 0  0  1  0  1  1  0  1  0 X+1 X+1  X  X X+1  1  1  1  0  1  1  X  X  0
 0  0  0  1  1  0  1  1  1  0  1  X X+1  0 X+1  1  X  1 X+1  X  X X+1  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  X  X  X  0  0  X
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  0  0  0  0  0  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+169x^16+354x^18+674x^20+824x^22+902x^24+652x^26+388x^28+88x^30+40x^32+2x^34+2x^36

The gray image is a linear code over GF(2) with n=46, k=12 and d=16.
This code was found by Heurico 1.16 in 0.429 seconds.