The generator matrix

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

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+72x^43+235x^44+206x^45+321x^46+514x^47+700x^48+828x^49+780x^50+900x^51+908x^52+804x^53+569x^54+504x^55+390x^56+176x^57+106x^58+52x^59+57x^60+30x^61+13x^62+6x^63+13x^64+4x^65+2x^66+1x^70

The gray image is a linear code over GF(2) with n=204, k=13 and d=86.
This code was found by Heurico 1.16 in 5.51 seconds.