The generator matrix

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

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+140x^17+651x^18+1560x^19+2640x^20+5140x^21+7196x^22+9954x^23+10613x^24+10252x^25+7496x^26+5132x^27+2559x^28+1414x^29+528x^30+186x^31+58x^32+12x^33+1x^34+1x^36+2x^37

The gray image is a linear code over GF(2) with n=96, k=16 and d=34.
This code was found by Heurico 1.13 in 12.3 seconds.