The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+189x^40+118x^42+8x^43+565x^44+72x^45+714x^46+288x^47+1611x^48+672x^49+1700x^50+1008x^51+2460x^52+1008x^53+1780x^54+672x^55+1613x^56+288x^57+702x^58+72x^59+530x^60+8x^61+98x^62+160x^64+8x^66+28x^68+10x^72+1x^76

The gray image is a linear code over GF(2) with n=208, k=14 and d=80.
This code was found by Heurico 1.16 in 16.2 seconds.