The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+122x^45+230x^46+568x^47+527x^48+740x^49+749x^50+910x^51+758x^52+938x^53+527x^54+704x^55+514x^56+404x^57+195x^58+162x^59+46x^60+32x^61+27x^62+20x^63+10x^64+4x^65+4x^67

The gray image is a linear code over GF(2) with n=208, k=13 and d=90.
This code was found by Heurico 1.16 in 2.99 seconds.