The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  1  0  1  1  1  1  0
 0  1  1  0  1  1  0  1  1  X X+1  1  0 X+1  1  0 X+1  1  0  0 X+1  0  1
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  X  X  X  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  X  0  0  X  X  X  0  X  0  0  X
 0  0  0  0  0  X  0  0  0  0  0  X  X  0  0  X  0  0  X  X  0  X  X
 0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  0  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  0  0  X  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  0  0  X  0  0  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+95x^16+120x^18+354x^20+408x^22+575x^24+232x^26+220x^28+8x^30+32x^32+2x^36+1x^40

The gray image is a linear code over GF(2) with n=46, k=11 and d=16.
This code was found by Heurico 1.16 in 0.148 seconds.