The generator matrix

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

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+29x^16+84x^17+135x^18+220x^19+407x^20+638x^21+876x^22+1098x^23+1187x^24+1102x^25+922x^26+666x^27+382x^28+218x^29+108x^30+62x^31+38x^32+6x^33+7x^34+2x^35+3x^36+1x^40

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 1.05 seconds.