The generator matrix

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

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+87x^16+430x^17+1135x^18+2796x^19+5216x^20+10352x^21+14678x^22+20104x^23+21242x^24+20452x^25+14657x^26+10256x^27+5304x^28+2736x^29+1074x^30+440x^31+86x^32+14x^33+7x^34+4x^35+1x^42

The gray image is a linear code over GF(2) with n=96, k=17 and d=32.
This code was found by Heurico 1.13 in 44.8 seconds.