The generator matrix

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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+76x^45+164x^46+290x^47+431x^48+466x^49+649x^50+844x^51+816x^52+836x^53+823x^54+768x^55+659x^56+476x^57+375x^58+204x^59+123x^60+88x^61+29x^62+30x^63+13x^64+10x^65+8x^66+8x^67+5x^68

The gray image is a linear code over GF(2) with n=212, k=13 and d=90.
This code was found by Heurico 1.16 in 3.63 seconds.