The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  0  X  X
 0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  1 X+1  X  1 X+1 X+1  1  1  0  0
 0  0  X  0  0  0  0  0  0  0  X  0  X  0  0  0  X  0  0  X  X  0  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  X  0  X  X
 0  0  0  0  X  0  0  0  0  0  X  X  0  X  X  X  0  0  0  X  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  0  X  X  0  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  0  0  X  X  0  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  0  X  X  0  0  X  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  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+166x^16+154x^18+512x^20+592x^22+1162x^24+660x^26+608x^28+128x^30+93x^32+2x^34+16x^36+2x^40

The gray image is a linear code over GF(2) with n=48, k=12 and d=16.
This code was found by Heurico 1.16 in 0.544 seconds.