The generator matrix

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

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+459x^20+1004x^22+1229x^24+938x^26+413x^28+40x^30+10x^32+2x^34

The gray image is a linear code over GF(2) with n=96, k=12 and d=40.
This code was found by Heurico 1.11 in 14.5 seconds.