The generator matrix

 1  0  0  0  0  0  1  1  1  1  0  1  X  1  X  X  X  1  1  1  1  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  X  X  1  1  1  X  1  1 X+1  1  X
 0  0  1  0  0  0  0 X+1  0  1  1  0  X X+1  1  X X+1  1 X+1  X  1  X  0  0
 0  0  0  1  0  0  0  1  1  X  1  X  0  1 X+1 X+1 X+1  X X+1  1 X+1  X  1  0
 0  0  0  0  1  0  1  0 X+1  1 X+1 X+1  X  1  X  0  X  X  X  1  X  0  X  X
 0  0  0  0  0  1  1 X+1  X  X  1  X  1 X+1 X+1  0  X  0  X  1  X X+1 X+1 X+1
 0  0  0  0  0  0  X  X  0  0  X  X  X  0  0  X  X  0  0  X  X  0  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+77x^16+148x^17+266x^18+428x^19+492x^20+554x^21+726x^22+854x^23+909x^24+940x^25+829x^26+730x^27+503x^28+316x^29+205x^30+90x^31+65x^32+24x^33+21x^34+10x^35+1x^36+2x^37+1x^38

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 2.07 seconds.