The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  1  X  1  1  1  1  1  1  1  1  1  1  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  0 X^2 X^2+X  0  0 X^2+X  0 X^2  0  0
 0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0
 0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  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+45x^16+34x^18+16x^19+101x^20+80x^21+141x^22+416x^23+366x^24+416x^25+177x^26+80x^27+90x^28+16x^29+18x^30+36x^32+12x^34+1x^36+1x^38+1x^42

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 0.0699 seconds.