The generator matrix

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

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+62x^14+267x^16+665x^18+1123x^20+1937x^22+2002x^24+1194x^26+646x^28+224x^30+50x^32+13x^34+7x^36+1x^38

The gray image is a linear code over GF(2) with n=46, k=13 and d=14.
This code was found by Heurico 1.16 in 2.83 seconds.