The generator matrix

 1  0  1  1  1 X^2  1  0  1  1 X^2  1 X^2  1  0  1  1  1  1  1 X^2+X X^2+X  1 X^2  1 X^2+X  1  1  X
 0  1  1  0  1  1 X^2  1  0 X+1  1 X+1  1 X^2  1 X^2+1 X^2+X+1  1  0 X^2+X  1  1  X  1  0  1 X+1 X^2 X^2+X
 0  0  X  0  0  0  0  0  0 X^2 X^2  X  X X^2+X X^2+X X^2+X X^2  X  X  X X^2+X  X X^2 X^2+X X^2+X X^2+X  0 X^2  0
 0  0  0  X  0  0 X^2 X^2+X X^2+X  0 X^2+X X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X  0  0 X^2+X  X X^2  0 X^2+X X^2+X  0
 0  0  0  0  X X^2+X X^2+X  X X^2+X  0 X^2 X^2+X  0 X^2 X^2+X  0  0  X X^2+X X^2  X X^2+X X^2  0 X^2+X X^2+X  X X^2  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+269x^24+96x^25+426x^26+256x^27+908x^28+320x^29+726x^30+256x^31+541x^32+96x^33+118x^34+68x^36+10x^38+5x^40

The gray image is a linear code over GF(2) with n=116, k=12 and d=48.
This code was found by Heurico 1.16 in 52.7 seconds.