The generator matrix

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

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+92x^16+126x^17+290x^18+438x^19+634x^20+1178x^21+1708x^22+2298x^23+2682x^24+2382x^25+1822x^26+1294x^27+618x^28+382x^29+250x^30+62x^31+65x^32+28x^33+24x^34+4x^35+4x^36+2x^38

The gray image is a linear code over GF(2) with n=96, k=14 and d=32.
This code was found by Heurico 1.16 in 4.15 seconds.