The generator matrix

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

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+80x^45+333x^46+400x^47+837x^48+500x^49+953x^50+556x^51+1025x^52+642x^53+859x^54+468x^55+689x^56+274x^57+309x^58+100x^59+95x^60+38x^61+8x^62+12x^63+9x^64+2x^65+2x^66

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 2.04 seconds.