The generator matrix

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

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+41x^24+64x^25+81x^26+142x^27+142x^28+134x^29+137x^30+100x^31+68x^32+52x^33+19x^34+14x^35+17x^36+6x^37+3x^38+2x^40+1x^44

The gray image is a linear code over GF(2) with n=116, k=10 and d=48.
This code was found by Heurico 1.16 in 0.0354 seconds.