The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  X  1  0 X^2+X  X  1  1  1  1 X^2+X  1  0  1 X^2+X  1  1  1  X  1  1  0  X  1  X  1  1  1  X  0  1 X^2 X^2+X X^2+X  1 X^2+X X^2+X  1  1  1  1 X^2  1 X^2+X X^2 X^2  1  1  1 X^2+X
 0  1  0  0  1  1  1 X^2  0  X X^2+X  1  1  1  1 X^2+X+1 X^2+X X^2+X+1  X  1 X^2+1  1 X+1  0  1  X X^2+X  1 X+1 X^2+X  1  1 X+1 X^2 X+1  0 X^2+1  1  1  1 X^2  1  1 X^2+X  X X^2+X X^2+1 X^2+1  0 X^2+1  1  X  1  1  1 X^2+X  X X^2+X+1  1
 0  0  1 X+1 X^2+X+1  0 X+1  X X^2+1  1  1  1 X^2+X X+1  1  X X+1 X+1  X  0  0 X^2 X^2+1  1 X^2+X X^2+1 X+1  X  0 X^2  1 X^2+1 X+1  1 X^2+1 X^2+X  X X^2+X+1 X^2+1  1  1 X^2 X^2+X+1 X^2+X+1  1  1  X X^2+X  0 X^2+X+1  0 X^2 X^2+X  0  1  1 X+1  X X^2+X+1
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  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+232x^52+212x^53+636x^54+488x^55+871x^56+580x^57+870x^58+568x^59+961x^60+556x^61+734x^62+440x^63+465x^64+172x^65+230x^66+40x^67+74x^68+16x^69+22x^70+15x^72+4x^74+5x^76

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 3.4 seconds.