The generator matrix

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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+190x^53+144x^54+556x^55+189x^56+622x^57+248x^58+562x^59+158x^60+470x^61+110x^62+342x^63+104x^64+222x^65+36x^66+70x^67+25x^68+28x^69+6x^70+6x^71+2x^72+4x^73+1x^76

The gray image is a linear code over GF(2) with n=236, k=12 and d=106.
This code was found by Heurico 1.16 in 0.773 seconds.