The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  0  1  X  0  1  0  0  1  0
 0  1  0  0  1  1  1  0  0  1 X+1  1  1  X  0  0 X+1  1  1  1  1  1  1  1
 0  0  1  1  1  0  1  0  1  1  0  X X+1  1  0  1  0  1  0  1  0  X  1  X
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  0  0  0  0  0  X  X  0  X
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  0  X  0  X  0  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  X  X  X  X  0  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  X  X  0  X  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  0  X  0  X  0  0  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  X  0  0  X  X  0  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+253x^16+280x^18+1062x^20+1384x^22+2157x^24+1528x^26+972x^28+376x^30+146x^32+16x^34+14x^36+3x^40

The gray image is a linear code over GF(2) with n=48, k=13 and d=16.
This code was found by Heurico 1.16 in 44.2 seconds.