The generator matrix

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

generates a code of length 51 over Z2[X]/(X^3) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+102x^43+284x^44+578x^45+789x^46+1232x^47+1293x^48+1518x^49+1468x^50+1822x^51+1568x^52+1738x^53+1255x^54+1016x^55+683x^56+498x^57+258x^58+152x^59+70x^60+36x^61+2x^62+12x^63+5x^64+4x^66

The gray image is a linear code over GF(2) with n=204, k=14 and d=86.
This code was found by Heurico 1.13 in 2.8 seconds.