The generator matrix
1 0 1 1 1 X^2+X 1 1 0 1 X X^2 1 1 1 1 1 X^2 0 1 1 1 1 X^2
0 1 1 0 X^2+X+1 1 X X+1 1 0 1 1 X^2+1 X+1 1 X^2+X X^2+1 1 1 1 X^2+X X^2+X X^2+1 X
0 0 X 0 X^2+X X^2 0 0 X X 0 X X^2+X X^2 X^2 X^2+X X^2+X 0 X^2+X 0 X^2 0 X^2+X X^2
0 0 0 X 0 X^2 X^2+X 0 X X^2+X X^2+X X^2 X X^2+X 0 X^2 X^2+X X 0 X 0 X^2 X^2+X X
0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 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+195x^20+108x^21+280x^22+296x^23+352x^24+240x^25+284x^26+120x^27+128x^28+4x^29+24x^30+11x^32+4x^34+1x^36
The gray image is a linear code over GF(2) with n=96, k=11 and d=40.
This code was found by Heurico 1.16 in 1.4 seconds.