The generator matrix

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

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+36x^20+110x^21+157x^22+162x^23+159x^24+128x^25+109x^26+106x^27+30x^28+2x^29+11x^30+2x^31+6x^32+3x^34+2x^35

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 0.0186 seconds.