The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  X  1  X  1  0  1  0  X  1
 0  X  0  0  0  0  0  0  0  0  X X^2+X X^2+X  X X^2+X X^2  0 X^2 X^2+X X^2 X^2+X  X  X X^2
 0  0  X  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2+X X^2+X X^2+X X^2+X X^2  X  X X^2+X  0
 0  0  0  X  0  0  0  X X^2+X X^2+X  0  X X^2  X X^2  0  X  X X^2+X  X  X X^2+X X^2  0
 0  0  0  0  X  0  X  X  X  0 X^2+X X^2  X  X  0 X^2+X X^2+X  0  X X^2  X  0 X^2+X  0
 0  0  0  0  0  X  X X^2 X^2+X X^2+X X^2 X^2  X  X X^2+X X^2 X^2 X^2 X^2+X  X  0  0  X  X
 0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0

generates a code of length 24 over Z2[X]/(X^3) who�s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+78x^16+148x^17+289x^18+406x^19+685x^20+1144x^21+1724x^22+2336x^23+2585x^24+2440x^25+1833x^26+1252x^27+667x^28+344x^29+231x^30+96x^31+76x^32+20x^33+18x^34+6x^35+4x^36+1x^38

The gray image is a linear code over GF(2) with n=96, k=14 and d=32.
This code was found by Heurico 1.16 in 4.49 seconds.