The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  1  X  0  X  1  0  X  1  1  X  1  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2  0 X^2  X  X X^2  X  0 X^2+X  0 X^2  X  X X^2  0
 0  0  X  0  X  X X^2+X  0  0  0  X X^2+X  X X^2  X  X  X X^2+X  0  0 X^2 X^2+X X^2+X  X
 0  0  0  X  X  0 X^2+X  X  0  X X^2+X  0 X^2 X^2  0 X^2 X^2  X  X X^2  X X^2+X  X  X
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 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+182x^16+462x^18+64x^19+1204x^20+576x^21+2460x^22+1408x^23+3580x^24+1408x^25+2552x^26+576x^27+1300x^28+64x^29+388x^30+125x^32+26x^34+8x^36

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 3.8 seconds.