The generator matrix

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

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+347x^16+904x^18+2011x^20+2878x^22+3862x^24+3300x^26+1946x^28+800x^30+270x^32+52x^34+11x^36+2x^38

The gray image is a linear code over GF(2) with n=48, k=14 and d=16.
This code was found by Heurico 1.16 in 52.6 seconds.