The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  0  0  X  0  0  X  0  X  1  1
 0  1  0  1  0  1  1  0  X  1 X+1  1  1  0  1  1  1  1  0  X  1  1  0  0
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  1  0  X  1 X+1  1  1  0  X  0  0
 0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  X  0  X  0  0  0  X  0  0
 0  0  0  0  X  0  0  0  X  0  0  X  X  X  0  X  X  0  0  0  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  0  X  0  X  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  X  0  0  X  X  X
 0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  0  X  X  0  0  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+42x^16+120x^18+256x^20+388x^22+436x^24+404x^26+236x^28+108x^30+49x^32+4x^34+4x^36

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 0.114 seconds.