The generator matrix

 1  0  0  0  1  1  1  1 X^2  1  0  X  1  1  0  1  X X^2  X  1  1  1  1  1  1  1  1  1  X
 0  1  0  0  0  1 X^2+1  X  1  1  1 X^2 X^2+X  1  1  0 X^2+X  X  1 X^2+X  X X+1  1 X^2+X+1 X^2 X+1  1 X+1  1
 0  0  1  0  0 X^2  1 X^2+1 X^2+X+1 X+1 X^2+X  1  1  X X^2+1 X^2+1  X  1 X^2+X+1 X^2 X^2+X+1 X^2+X+1 X^2+X  0 X^2+X+1 X^2+X  1 X+1  X
 0  0  0  1  1  0 X^2+1 X^2+X  1 X^2+X X+1  1 X^2+X+1 X^2+1  X  1  1  X X^2 X^2+1  1  1 X^2+X X^2+X+1  X  X  X X+1 X+1
 0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 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+500x^24+1558x^26+2024x^28+2118x^30+1504x^32+418x^34+64x^36+2x^38+2x^40+1x^48

The gray image is a linear code over GF(2) with n=116, k=13 and d=48.
This code was found by Heurico 1.11 in 10.8 seconds.