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 X^2  X  X  0  1  1  1  1  1  X  X  X  0  1  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2+X X^2  0  X X^2 X^2+X  X  X X^2  X  X  X  0  0 X^2  0  0 X^2 X^2 X^2+X X^2+X  0  X  0 X^2  X  X  0  0 X^2+X  0 X^2+X X^2  0 X^2  0 X^2 X^2+X  X
 0  0  X  0  0  0  X X^2+X  X  0  0  0  X  X  0  X X^2  X X^2+X X^2+X  0 X^2  0 X^2 X^2+X X^2 X^2  X X^2+X  0  X  X X^2+X X^2  0  X  X  0 X^2 X^2  X X^2 X^2+X X^2+X X^2+X X^2 X^2+X X^2+X X^2+X  0  X  0
 0  0  0  X  0  X  X X^2+X  0  X  X X^2  0 X^2 X^2+X  X  X  0 X^2+X X^2+X X^2  X  0  0 X^2  X  0  X  0 X^2+X X^2+X  X  X  0 X^2+X X^2 X^2  X X^2 X^2+X X^2  0 X^2  0  X  0 X^2 X^2 X^2+X X^2 X^2+X X^2
 0  0  0  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2  X  0  0  X X^2  0 X^2+X X^2  X  X  X  X  0  0  0 X^2+X X^2+X  0 X^2+X  0  X  X  X X^2 X^2 X^2 X^2+X  X X^2+X X^2  0 X^2+X X^2+X  X  X  X
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 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 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0  0  0  0  0  0 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+212x^42+534x^44+8x^45+788x^46+72x^47+1077x^48+632x^49+2153x^50+1336x^51+2794x^52+1336x^53+2088x^54+632x^55+1221x^56+72x^57+718x^58+8x^59+434x^60+172x^62+76x^64+13x^66+6x^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 19.3 seconds.