The generator matrix

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

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+162x^53+207x^54+394x^55+413x^56+442x^57+382x^58+428x^59+292x^60+426x^61+232x^62+230x^63+154x^64+116x^65+58x^66+66x^67+28x^68+34x^69+17x^70+7x^72+2x^73+2x^75+2x^77+1x^80

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 0.778 seconds.