The generator matrix

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

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+86x^14+178x^15+408x^16+568x^17+951x^18+1300x^19+1872x^20+2580x^21+3018x^22+3580x^23+3622x^24+3628x^25+3105x^26+2456x^27+1922x^28+1356x^29+952x^30+530x^31+361x^32+188x^33+79x^34+20x^35+6x^36+1x^42

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 29.2 seconds.