The generator matrix

 1  0  0  1  1  1  X  0  1  1  1 X^2+X  1 X^2 X^2+X X^2+X  1  1  0  1  1  1 X^2  0  1 X^2 X^2+X X^2+X X^2+X X^2+X  1  0  0  1  1  1  1 X^2+X  1  1  1  1 X^2  1  1 X^2+X X^2  1  1  X  1  1  1
 0  1  0  0  1 X^2+X+1  1  1  X  X X+1  1  1  X  1  1 X^2 X^2+1 X^2+X X^2  1  0  1  1 X+1  0  1  1  X  X  0  1  1 X^2+1 X^2+X X^2+X  1  1  X X^2+X+1 X+1 X+1  1 X^2  1 X^2+X  1 X+1  X  1 X^2  0  0
 0  0  1  1  1  0  1 X+1 X+1  X X^2+X+1  0 X^2  1 X+1 X^2+X X+1  1  1 X^2+X X^2+X X^2+1  1 X^2+X X^2+1  1 X^2+X  1  1  1  0 X^2+X+1 X^2+1 X+1  X X^2+1 X+1  X X^2+1 X^2+X X^2+X  0 X^2+X+1  0  1  1 X^2 X^2+X X^2 X^2  1  0 X+1
 0  0  0  X  0 X^2+X X^2  0  X X^2 X^2  0  X  0 X^2  0 X^2+X X^2+X X^2+X X^2+X X^2 X^2  X  X  X X^2+X X^2+X  X  0  X X^2 X^2 X^2  X X^2+X  0  X X^2+X  0 X^2+X X^2+X X^2+X  X  0  0 X^2 X^2+X  0 X^2 X^2  X  X  0
 0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  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+150x^46+264x^47+512x^48+584x^49+670x^50+760x^51+811x^52+884x^53+726x^54+844x^55+597x^56+464x^57+369x^58+240x^59+171x^60+52x^61+55x^62+4x^63+14x^64+13x^66+6x^68+1x^70

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 2.76 seconds.