The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  1  X  0  X X^2  X  1 X^2  1
 0  X  0  0  0  0  0  0  0  X  X  X X^2+X  X X^2 X^2+X X^2  0 X^2  X X^2+X  X  0  0
 0  0  X  0  0  0  X X^2+X  X  X X^2+X X^2  X  X X^2+X  0  X  0 X^2  0  0  0 X^2  0
 0  0  0  X  0  X  X  X  0 X^2  X X^2+X X^2 X^2+X X^2+X X^2+X X^2+X X^2  X X^2 X^2 X^2+X X^2  0
 0  0  0  0  X  X  0  X X^2+X X^2 X^2+X  X X^2+X  0  0  X X^2+X  X X^2+X  X  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  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+64x^16+86x^17+180x^18+250x^19+381x^20+626x^21+839x^22+1100x^23+1145x^24+1066x^25+867x^26+636x^27+403x^28+254x^29+149x^30+60x^31+50x^32+16x^33+13x^34+2x^35+4x^36

The gray image is a linear code over GF(2) with n=96, k=13 and d=32.
This code was found by Heurico 1.16 in 1.12 seconds.