The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1 X^2+X  1  1 X^2+X  1  1  1 X^2  1  1 X^2 X^2+X  1  1  1 X^2 X^2  X  1  1 X^2  1 X^2+X  1  1  1  1  1 X^2+X X^2  1  1  1  1  0  1  1  1  1 X^2 X^2+X  0  1  0  0  1
 0  1  1  0 X^2+X+1  1  X X+1  1 X^2+X  1 X^2+1 X^2+X+1  1 X^2+X  1  1 X^2  0 X^2+X+1  1 X^2+1 X^2+X  1  1  1  X X^2+1  1  1  1  1 X^2  1  0  1  X  1  0  1 X^2+X+1  1  1  X X^2+1 X^2 X^2  X X^2+X+1 X^2+1 X^2+X X^2+1 X^2  1  1 X^2+1  X  1  0
 0  0  X  0 X^2+X  0  0  X X^2  0 X^2  X  0 X^2+X  X X^2  X X^2+X X^2+X X^2 X^2+X  0  X  X  X X^2  0  X  X X^2  0  X  X  X  0 X^2+X  X  0 X^2 X^2+X X^2 X^2+X  0  0  X  X X^2 X^2 X^2  0  0 X^2 X^2  X X^2 X^2+X  X  X  0
 0  0  0  X  0  0  X  X X^2+X X^2  X  X  X X^2+X X^2+X  X X^2  0 X^2+X  0 X^2  0 X^2 X^2  X  X  X  0  0 X^2  0 X^2+X X^2 X^2+X X^2 X^2+X  X  X  X X^2  0 X^2+X X^2+X  X  X X^2+X  X  X  0 X^2+X  0  0  X  X X^2+X X^2+X X^2+X  X  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  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+41x^50+94x^51+206x^52+334x^53+397x^54+536x^55+623x^56+708x^57+817x^58+832x^59+775x^60+714x^61+625x^62+458x^63+381x^64+252x^65+126x^66+104x^67+51x^68+38x^69+38x^70+22x^71+6x^72+4x^74+2x^75+4x^76+2x^77+1x^80

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 3.79 seconds.