The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  X  X  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  0  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  X  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  0  0  X  0  X  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  0  X  X  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  X  X
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  X  0  0  X  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  0  0  X  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  0  X  0  X  0  X  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+176x^16+32x^18+256x^20+224x^22+622x^24+224x^26+368x^28+32x^30+95x^32+16x^36+2x^40

The gray image is a linear code over GF(2) with n=48, k=11 and d=16.
This code was found by Heurico 1.16 in 0.161 seconds.