The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  1  0  0  X  X  1  1  1  1  1  1  X  0  1  1  1 X^2  1  1 X^2+X  1  1 X^2  1 X^2  0  1  0 X^2+X  1  1 X^2+X  1  X  1  1  1  1  1  1  X  1
 0  1  0  0  X X^2 X^2+X  1 X+1 X^2+1  1 X^2+1  1 X^2+X  1  1 X^2+X+1 X^2+1 X^2+X X^2+X X^2 X+1 X^2+X  1  0  X X^2+X+1 X^2  1  0  0 X^2+1 X^2+X+1  X X^2+1  1  1  0 X^2 X^2+X X^2 X+1  1 X^2  1  1 X^2+X+1 X^2+1 X^2+X  X X+1  1  0
 0  0  1  0  X X^2+1  1 X^2+1  0 X^2+1 X^2 X^2+X+1 X+1  1 X^2 X^2+X X+1 X^2+X X^2+1 X^2+X+1  X X^2  0 X^2+X+1  0 X^2+1  0  1 X^2+X+1 X^2+X  1  0 X^2+X+1  1 X^2 X^2+X  1 X+1 X^2+X  X  0 X+1  0 X^2+X+1 X+1  1 X^2+X X^2  1 X^2+X+1 X+1 X+1  0
 0  0  0  1 X+1  1  X X^2+1 X^2+X X^2+X+1 X^2+X+1 X^2 X^2+X X^2+X+1 X^2+1  1 X^2+1 X^2+1  0  1  0  0  1 X^2+X X^2+1 X+1  X X+1  X X^2+X  X  X  X X^2+X X^2+1 X^2+X  1 X^2+X+1  1  1 X^2+X+1  0 X^2+X X^2 X^2 X+1  0 X+1 X^2+1 X^2+X X^2+1  X  0
 0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 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+101x^46+300x^47+464x^48+662x^49+710x^50+884x^51+732x^52+810x^53+655x^54+792x^55+550x^56+526x^57+439x^58+276x^59+146x^60+78x^61+28x^62+20x^63+9x^64+4x^65+3x^66+2x^68

The gray image is a linear code over GF(2) with n=212, k=13 and d=92.
This code was found by Heurico 1.16 in 2.04 seconds.