The generator matrix

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

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+126x^52+346x^53+558x^54+632x^55+775x^56+678x^57+803x^58+722x^59+706x^60+570x^61+717x^62+464x^63+405x^64+288x^65+205x^66+98x^67+48x^68+32x^69+5x^70+4x^71+1x^72+6x^73+2x^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 1.11 in 0.938 seconds.