The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  X  X  1  X
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 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+176x^16+32x^18+256x^20+224x^22+2670x^24+224x^26+368x^28+32x^30+95x^32+16x^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 0.306 seconds.