The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X X^2  X  1  1  1  X X^2 X^2  0  X
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X  X X^2 X^2+X  X  X  0 X^2+X  0 X^2 X^2+X X^2+X  X  X X^2  X  X  0  0
 0  0  X  0  0 X^2 X^2+X  X  X  X  X  X X^2+X X^2  X X^2  0 X^2  X X^2  X X^2 X^2+X  0  0  0  0  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^2+X X^2+X X^2 X^2 X^2  X  X  0 X^2+X  X  X  X X^2 X^2+X X^2  0
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2 X^2  0  X  X  X  0  0  0  X  X X^2  X  X X^2 X^2+X  0  X  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+217x^24+68x^25+88x^26+244x^27+274x^28+392x^29+84x^30+264x^31+203x^32+52x^33+80x^34+4x^35+70x^36+4x^38+3x^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 0.12 seconds.