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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+214x^42+499x^44+824x^46+80x^47+1175x^48+528x^49+2120x^50+1440x^51+2682x^52+1440x^53+2078x^54+528x^55+1251x^56+80x^57+708x^58+457x^60+194x^62+76x^64+6x^66+2x^68+1x^88

The gray image is a linear code over GF(2) with n=208, k=14 and d=84.
This code was found by Heurico 1.16 in 15.7 seconds.