The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+73x^24+96x^25+228x^26+256x^27+210x^28+320x^29+270x^30+256x^31+145x^32+96x^33+64x^34+18x^36+14x^38+1x^40

The gray image is a linear code over GF(2) with n=116, k=11 and d=48.
This code was found by Heurico 1.16 in 0.0839 seconds.