The generator matrix

 1  0  0  0  1  1  1  0  1  1  X  1  1  0  X  0  0  X  0  1  1  1  1  1
 0  1  0  0  0  1  1  1  0  0  0 X+1 X+1  1  1  1  1  1  1 X+1  1  X  0  0
 0  0  1  0  1  1  0  1  0  1  1  1  0  X  1  0 X+1 X+1  0  X  0  0  1  0
 0  0  0  1  1  0  1  1  1  0  1  1  X  1  0  0 X+1  0  0  0  1 X+1  1  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  X  X  0  0  0  X  0  0  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  X  0  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  X  0  0  0  0  0  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  0  0  0  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  0  X  X  X  0  X  X  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+28x^14+62x^15+160x^16+260x^17+452x^18+652x^19+938x^20+1266x^21+1572x^22+1828x^23+1884x^24+1872x^25+1568x^26+1312x^27+972x^28+636x^29+444x^30+238x^31+131x^32+60x^33+28x^34+4x^35+10x^36+2x^37+4x^38

The gray image is a linear code over GF(2) with n=48, k=14 and d=14.
This code was found by Heurico 1.16 in 9.6 seconds.