The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+78x^43+360x^44+656x^45+1156x^46+1364x^47+2159x^48+2348x^49+3140x^50+3190x^51+3752x^52+3280x^53+3227x^54+2522x^55+2200x^56+1252x^57+1009x^58+472x^59+308x^60+136x^61+73x^62+50x^63+20x^64+8x^65+3x^66+4x^67

The gray image is a linear code over GF(2) with n=208, k=15 and d=86.
This code was found by Heurico 1.16 in 30.6 seconds.