The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  1  1  1  1  1  1  X  1  1  1
 0  1  1  0  1  1  0  1  1  X X+1  1  1 X+1 X+1 X+1 X+1 X+1 X+1  1  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0
 0  0  0  X  0  0  0  0  0  X  X  0  X  X  X  0  X  X  0  0  0  0  0  0
 0  0  0  0  X  0  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  X  0  X  0  X  X  0  X  0  X  0  X  0  0  0  0
 0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  0  0  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  X  X  0  0  X  X  0  X  X  X  X  0  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+78x^16+96x^18+32x^19+84x^22+224x^23+80x^24+224x^27+96x^28+72x^30+32x^31+1x^32+4x^38

The gray image is a linear code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0338 seconds.