The generator matrix

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

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+84x^16+48x^18+365x^20+208x^22+628x^24+208x^26+391x^28+48x^30+55x^32+11x^36+1x^44

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 0.12 seconds.