The generator matrix

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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+112x^47+254x^48+336x^49+424x^50+402x^51+468x^52+474x^53+319x^54+290x^55+281x^56+244x^57+165x^58+150x^59+93x^60+28x^61+33x^62+6x^63+4x^64+4x^65+3x^66+3x^68+2x^69

The gray image is a linear code over GF(2) with n=212, k=12 and d=94.
This code was found by Heurico 1.16 in 0.608 seconds.