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

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+192x^50+16x^51+448x^52+64x^53+634x^54+200x^55+868x^56+480x^57+1010x^58+560x^59+976x^60+424x^61+826x^62+232x^63+557x^64+48x^65+314x^66+16x^67+187x^68+8x^69+84x^70+30x^72+12x^74+4x^76+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 5.29 seconds.