The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  1  1  0  1 X^2+X  1  1  1 X^2+X  0
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2 X^2+X X+1  1 X^2+1  1 X^2+X X^2+1 X^2+X+1  1  1
 0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0
 0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  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 20.

Homogenous weight enumerator: w(x)=1x^0+79x^20+304x^22+266x^24+304x^26+56x^28+13x^32+1x^36

The gray image is a linear code over GF(2) with n=96, k=10 and d=40.
This code was found by Heurico 1.16 in 0.0191 seconds.