The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0
 0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  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  0 X^2 X^2  0  0  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 X^2  0 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0 X^2  0  0 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 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  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 X^2  0  0  0 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+97x^16+126x^20+128x^22+1325x^24+128x^26+180x^28+46x^32+14x^36+3x^40

The gray image is a linear code over GF(2) with n=96, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0794 seconds.