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.