The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  1  1  X  X  1  1  1  0  1  1  1  0  0
 0  1  0  0  0  0  0  0  1  1 X+1 X+1 X+1  1  X  X X+1  X  1 X+1  1  0  1  X
 0  0  1  0  0  0  1  1  1  1  X X+1  X  X  1  1 X+1  0  1  0  0  X  X  0
 0  0  0  1  0  1  1  0  1  0 X+1  1  X  1 X+1  1 X+1 X+1  0  1 X+1  X X+1  X
 0  0  0  0  1  1  0  1  1  X X+1  X  0  0  0  1 X+1  X X+1  X X+1 X+1  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  X  X  0  X  0  0  X
 0  0  0  0  0  0  X  0  0  X  X  0  0  0  X  X  X  0  X  X  X  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  X  X  0  X  X  0  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+155x^16+548x^18+980x^20+1392x^22+1939x^24+1552x^26+1012x^28+448x^30+128x^32+28x^34+8x^36+1x^40

The gray image is a linear code over GF(2) with n=48, k=13 and d=16.
This code was found by Heurico 1.16 in 1.96 seconds.