The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+40x^41+262x^42+848x^43+1420x^44+2844x^45+3764x^46+5838x^47+7450x^48+10468x^49+11133x^50+14510x^51+12993x^52+14842x^53+11839x^54+10892x^55+7389x^56+6130x^57+3579x^58+2284x^59+1203x^60+722x^61+305x^62+182x^63+68x^64+26x^65+30x^66+6x^67+4x^68

The gray image is a linear code over GF(2) with n=208, k=17 and d=82.
This code was found by Heurico 1.13 in 149 seconds.