The generator matrix

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

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+82x^17+165x^18+202x^19+295x^20+440x^21+788x^22+1308x^23+1564x^24+1336x^25+861x^26+476x^27+285x^28+176x^29+103x^30+60x^31+30x^32+14x^33+2x^34+2x^35+1x^38+1x^40

The gray image is a linear code over GF(2) with n=96, k=13 and d=34.
This code was found by Heurico 1.16 in 1.63 seconds.