The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1
 0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  X  X  0  0  0
 0  0  X  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  X  0  0  0  X
 0  0  0  X  0  0  0  X  0  X  X  0  0  0  X  0  X  X  X  X  X  0  X  X
 0  0  0  0  X  0  0  X  0  X  0  X  0  X  X  X  0  0  0  X  X  X  X  X
 0  0  0  0  0  X  0  X  X  0  0  X  0  X  0  0  0  X  X  0  X  X  X  0
 0  0  0  0  0  0  X  X  X  0  X  0  0  X  X  X  0  0  X  X  0  0  X  0

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+50x^20+32x^22+104x^24+32x^26+21x^28+15x^32+1x^44

The gray image is a linear code over GF(2) with n=48, k=8 and d=20.
This code was found by Heurico 1.16 in 1.26 seconds.