The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  X  X X^2  0  1  0  1  X  1  X  1  1  1
 0  X  0  X  0  0  X X^2+X  0 X^2  X  X X^2+X  X  X  X  0  X X^2+X  0 X^2+X X^2+X  0  0
 0  0  X  X  0 X^2+X  X  0 X^2  X X^2  X  0  X  0 X^2  X  0  0  0 X^2  0  0  0
 0  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  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+82x^16+100x^18+32x^19+268x^20+288x^21+402x^22+704x^23+328x^24+704x^25+434x^26+288x^27+262x^28+32x^29+86x^30+75x^32+2x^34+6x^36+2x^40

The gray image is a linear code over GF(2) with n=96, k=12 and d=32.
This code was found by Heurico 1.16 in 0.237 seconds.