The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1  1
 0  X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2  X  0 X^2 X^2 X^2+X  X X^2  0  0
 0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0
 0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0
 0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+6x^20+8x^21+19x^22+92x^23+17x^24+84x^25+10x^26+4x^27+8x^28+4x^29+2x^30+1x^46

The gray image is a linear code over GF(2) with n=96, k=8 and d=40.
This code was found by Heurico 1.16 in 0.00569 seconds.