The generator matrix

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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+102x^46+308x^47+480x^48+664x^49+649x^50+864x^51+724x^52+794x^53+747x^54+864x^55+585x^56+476x^57+334x^58+272x^59+158x^60+76x^61+53x^62+28x^63+4x^64+4x^65+3x^66+2x^69

The gray image is a linear code over GF(2) with n=212, k=13 and d=92.
This code was found by Heurico 1.11 in 0.796 seconds.