The generator matrix

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

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+100x^19+203x^20+390x^21+395x^22+670x^23+601x^24+668x^25+413x^26+368x^27+149x^28+94x^29+21x^30+14x^31+6x^32+3x^34

The gray image is a linear code over GF(2) with n=96, k=12 and d=38.
This code was found by Heurico 1.16 in 0.221 seconds.