The generator matrix

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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+216x^50+12x^51+450x^52+88x^53+575x^54+216x^55+832x^56+428x^57+1046x^58+568x^59+1047x^60+420x^61+823x^62+216x^63+524x^64+84x^65+315x^66+12x^67+186x^68+4x^69+84x^70+31x^72+11x^74+2x^78+1x^84

The gray image is a linear code over GF(2) with n=236, k=13 and d=100.
This code was found by Heurico 1.16 in 20.3 seconds.