The generator matrix

 1  0  1  1  1 X^2+X  1 X^2  1  1  X  1  0  1 X^2+X X^2 X^2+X X^2+X  1  1  X  1  X  1
 0  1  1 X^2+X X^2+X+1  1 X^2  1 X+1  X  1 X^2+1  1  X  1  1  1  1  1  0  1 X^2+1  X X+1
 0  0  X  0 X^2+X X^2  X  X  0 X^2+X X^2+X  0 X^2  X X^2 X^2+X X^2 X^2+X X^2+X  0  X  0  X  0
 0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  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+46x^20+102x^21+147x^22+168x^23+152x^24+158x^25+101x^26+56x^27+54x^28+26x^29+5x^30+3x^32+2x^33+3x^34

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 0.0196 seconds.