The generator matrix
1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 1 1 1 1 1 1 1 1 0 X^2
0 1 X+1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 X^2 X^2+X X X^2 0 X 0 X+1 X^2+X+1 X^2+X 1 1
0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2
0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0
generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+81x^22+93x^24+78x^26+1x^30+2x^36
The gray image is a linear code over GF(2) with n=96, k=8 and d=44.
This code was found by Heurico 1.16 in 0.00516 seconds.