The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  X X^2+X  1  X  1  1  1 X^2  1  1 X^2+X  0  1  1  1 X^2+X X^2+X  0  1 X^2+X  1 X^2  X X^2  1  1  0  1 X^2+X  0  0  1  1 X^2+X  1  0 X^2+X X^2+X  0  X  0  1  1  1  X X^2  1  1
 0  1  0  0  X X^2 X^2+X  1 X+1 X^2+1  1  X  1  1  1 X+1  X X^2+X+1  0 X+1  X  1  1 X+1 X^2  0 X^2  1  X X^2+1  1  0  1  1  1 X^2+X X^2+1  1 X+1  1  1  1  1  0  1 X^2+X X^2+X X^2  0  0  X  X X^2 X+1 X+1  1  1  X  0
 0  0  1  0  X X^2+1  1 X^2+1  0 X^2+1 X^2  1 X^2+1 X+1  X X+1 X^2+X+1 X^2+X  1 X^2+X  0  1 X+1 X^2+1 X^2+X+1 X^2+X  1  X  0 X^2+X+1 X^2  1 X^2+X+1  0  0 X^2 X^2+X+1  X  0 X+1 X^2 X^2+X  1  X X^2+X+1 X^2  1  1  1  1  1  1  X  1 X^2+1 X^2+X+1 X^2  1 X^2+X
 0  0  0  1 X+1  1  X X^2+1 X^2+X X^2+X+1 X^2+X+1 X+1 X^2+X X^2+X X^2+1  0 X^2+1 X^2+X+1 X^2+X X^2 X^2+X+1  0 X^2+1 X^2+X+1  X X^2+1 X^2+X+1 X^2+X+1  1 X+1  0 X^2+X+1  0 X^2+X+1 X^2+X+1 X^2+X X^2  0 X^2+X  X  X  X  X X^2 X^2+1  0  1  1 X^2  0 X^2+1 X^2+X  1 X+1 X^2+1 X^2  X  0  X
 0  0  0  0 X^2  0 X^2  0 X^2 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  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 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+114x^52+410x^53+430x^54+720x^55+646x^56+904x^57+661x^58+784x^59+656x^60+758x^61+520x^62+514x^63+331x^64+344x^65+167x^66+132x^67+43x^68+30x^69+12x^70+10x^71+2x^74+1x^76+2x^77

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 2.35 seconds.