The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 X 1 X 1 0 1 0 X 1
0 X 0 0 0 0 0 0 0 0 X X^2+X X^2+X X X^2+X X^2 0 X^2 X^2+X X^2 X^2+X X X X^2
0 0 X 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2+X X^2+X X^2+X X^2+X X^2 X X X^2+X 0
0 0 0 X 0 0 0 X X^2+X X^2+X 0 X X^2 X X^2 0 X X X^2+X X X X^2+X X^2 0
0 0 0 0 X 0 X X X 0 X^2+X X^2 X X 0 X^2+X X^2+X 0 X X^2 X 0 X^2+X 0
0 0 0 0 0 X X X^2 X^2+X X^2+X X^2 X^2 X X X^2+X X^2 X^2 X^2 X^2+X X 0 0 X X
0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 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+78x^16+148x^17+289x^18+406x^19+685x^20+1144x^21+1724x^22+2336x^23+2585x^24+2440x^25+1833x^26+1252x^27+667x^28+344x^29+231x^30+96x^31+76x^32+20x^33+18x^34+6x^35+4x^36+1x^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 4.49 seconds.