The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  0  1  X  1  0  1  X  0  X  1  1
 0  1  0  0  0  0  0  0  0  0  0  1  1  X  1  X  1  1  X  X  1  1 X+1  0
 0  0  1  0  0  0  0  0  1  1  X  1  X  X  1  0  0  0  0  1 X+1 X+1  0  0
 0  0  0  1  0  0  0  0  1  X  0  0  1  1 X+1  0  X  1  1 X+1  X  0  X  0
 0  0  0  0  1  0  0  0  1 X+1 X+1  X  0 X+1  1  1  1 X+1  X  X X+1  X  1  0
 0  0  0  0  0  1  0  1  0  1 X+1  X X+1  1  0 X+1  0  X  0  X X+1  X  1  0
 0  0  0  0  0  0  1  1 X+1  1  X  0  1  X  0  1  X  X  1 X+1  0  X  0  0
 0  0  0  0  0  0  0  X  X  0  X  X  0  0  0  X  X  X  0  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+74x^14+200x^15+349x^16+632x^17+950x^18+1350x^19+1872x^20+2488x^21+3054x^22+3476x^23+3716x^24+3568x^25+3155x^26+2488x^27+1910x^28+1432x^29+872x^30+532x^31+334x^32+200x^33+86x^34+18x^35+10x^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 1.11 in 8.75 seconds.