The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+188x^46+12x^47+191x^48+84x^49+269x^50+168x^51+318x^52+152x^53+237x^54+76x^55+139x^56+20x^57+115x^58+43x^60+19x^62+9x^64+4x^66+2x^68+1x^84

The gray image is a linear code over GF(2) with n=208, k=11 and d=92.
This code was found by Heurico 1.16 in 18.7 seconds.