The generator matrix

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

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+219x^16+220x^18+718x^20+764x^22+1155x^24+500x^26+416x^28+52x^30+48x^32+2x^36+1x^40

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 2.35 seconds.