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

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+48x^42+64x^43+158x^44+208x^45+287x^46+400x^47+446x^48+582x^49+706x^50+796x^51+829x^52+824x^53+692x^54+588x^55+478x^56+356x^57+251x^58+180x^59+114x^60+72x^61+49x^62+20x^63+19x^64+6x^65+10x^66+3x^68+4x^70+1x^74

The gray image is a linear code over GF(2) with n=208, k=13 and d=84.
This code was found by Heurico 1.16 in 4.19 seconds.