The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  1  1  1  1  X  1  X  0  X  0  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1 X+1  1 X+1  0  X  1  1  1  X X+1  0
 0  0  1  0  0  0  1  1  1  1  1  0  0 X+1  0  1  0  X  X  1  X  1  X  0
 0  0  0  1  0  1  1  0  1  0  1  1  1  1  0  0  1  X  1 X+1  0  1  0  0
 0  0  0  0  1  1  0  1  1  0  1  1  0  X  1  1 X+1  1  0 X+1 X+1  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  X  0  0  X  X  0  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  X  X  X  0  0  X

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+85x^14+98x^15+348x^16+498x^17+899x^18+1238x^19+1902x^20+2598x^21+3108x^22+3724x^23+3678x^24+3772x^25+3118x^26+2660x^27+1940x^28+1236x^29+901x^30+466x^31+307x^32+82x^33+79x^34+6x^35+14x^36+6x^37+2x^38+2x^40

The gray image is a linear code over GF(2) with n=48, k=15 and d=14.
This code was found by Heurico 1.16 in 19.1 seconds.