The generator matrix

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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+189x^52+312x^53+482x^54+652x^55+723x^56+756x^57+736x^58+808x^59+682x^60+640x^61+624x^62+556x^63+421x^64+260x^65+138x^66+96x^67+46x^68+16x^69+34x^70+14x^72+2x^74+3x^76+1x^80

The gray image is a linear code over GF(2) with n=236, k=13 and d=104.
This code was found by Heurico 1.16 in 3.25 seconds.