The generator matrix

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

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+256x^43+758x^44+1248x^45+2215x^46+2998x^47+3935x^48+4882x^49+6163x^50+6282x^51+7420x^52+6810x^53+6530x^54+4930x^55+4100x^56+2944x^57+1905x^58+1040x^59+586x^60+294x^61+140x^62+44x^63+32x^64+10x^65+4x^66+2x^67+4x^69+3x^70

The gray image is a linear code over GF(2) with n=208, k=16 and d=86.
This code was found by Heurico 1.13 in 39.5 seconds.