The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+66x^43+313x^44+658x^45+1218x^46+1582x^47+1871x^48+2566x^49+3005x^50+3322x^51+3450x^52+3348x^53+3086x^54+2638x^55+2248x^56+1480x^57+808x^58+564x^59+285x^60+130x^61+72x^62+20x^63+23x^64+10x^65+3x^66+1x^80

The gray image is a linear code over GF(2) with n=208, k=15 and d=86.
This code was found by Heurico 1.16 in 30.9 seconds.