The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1 X^2  1 X^2+X  1  0  1  1  X  1  0  1 X^2+X  1  1  1  1  X  1 X^2+X X^2  0 X^2+X  1 X^2 X^2 X^2+X  1 X^2+X  1 X^2  X  X  X  1  0  1 X^2+X  1 X^2
 0  1  0  0  0  0  0 X^2 X^2  1  1  1  1  1  1 X+1 X^2+X X^2+X+1 X^2+X  X X^2  1 X^2+1  1  X  X X^2+X+1 X^2+X+1  1  X  1  0 X^2+X X^2 X^2+X  1  0 X^2+X X+1  1 X^2+X+1  1  0  1  1 X+1  0  1  1  0  X
 0  0  1  0  0 X^2  1 X^2+1  1  0  1 X+1 X^2+X+1 X^2+1  0  X  1  X X^2+X+1  1  1  0  X X^2+X  0 X^2+X X^2+X+1  1  1 X^2+1 X+1  X  X X^2 X^2+X+1 X^2  1  1 X^2+X  1 X^2+1 X^2+X+1  1  1 X^2+X+1  1  X X^2+1  X X^2+X X^2+X
 0  0  0  1  0 X^2+1  1  0  1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X  1  0 X^2+X+1 X+1 X^2+1  X  0 X^2+1 X^2+X X^2 X^2+1 X+1 X^2  0  1  0  1 X^2+X+1  X X^2+X+1 X^2+X+1  X X^2 X^2+1  1 X^2+X+1  0 X^2+X  X  1 X^2+1 X^2+1  0  1
 0  0  0  0  1  1 X^2  1  1 X^2+1 X^2  1 X+1  0  1  0 X^2+1 X+1 X^2+X X^2+X X^2+X+1  X X^2+X X^2+X+1 X^2  1  1 X^2+X X^2+1 X+1 X^2  X  1 X^2+X+1 X^2+X+1 X^2+X  0  1  X  0 X^2+X+1 X^2+X X^2+X  1 X^2+1 X^2+1  1 X^2+X+1  X X^2+1  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+268x^43+691x^44+1182x^45+1532x^46+2136x^47+2550x^48+3004x^49+3093x^50+3708x^51+3300x^52+3188x^53+2598x^54+2016x^55+1461x^56+994x^57+497x^58+328x^59+121x^60+58x^61+24x^62+8x^63+2x^64+6x^65+2x^68

The gray image is a linear code over GF(2) with n=204, k=15 and d=86.
This code was found by Heurico 1.13 in 10.1 seconds.