The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^2+X  1  1  X X^3+X^2+X  1  1  0  1 X^2+X X^2+X  1 X^3+X^2  1  1 X^3+X^2+X  1 X^3  1 X^3+X^2 X^3+X^2+X  1 X^2+X  1  1 X^3+X^2  1  1  1  1  1  0 X^3 X^2+X X^2  1 X^3+X  1 X^3+X^2+X  X  1
 0  1  0  0  0 X^3+1 X^3+1  1 X^3+X^2+X X^3+X X^3+X^2+X X+1 X^2+1  1  1 X+1 X^3+X^2+X  1 X^2  1  1 X^3+1  1 X^2+1 X^3+X+1 X^2+X X^3+X^2 X^3+X  0  X  1 X^3+X X^3+X^2 X^2+1 X^3+X^2+X  1 X^2 X^3+X^2+X X^3+X^2+1 X^3+X X^3+X+1 X^3+X X^3+X X^3+X^2+X  1 X^3+X^2+1  1  1  1  0 X^3
 0  0  1  0  1  1 X^2 X^2+1  0 X^3+1  1 X^2+1  X X^2 X^3+X^2+X+1 X^3+X^2+X  1 X^2+X X^3+X^2 X^3+X^2+1 X^2+X+1 X^2+X+1 X^3 X^3+X^2+X X^3+X+1  0 X^3+X  1 X^3+1  1 X^2+X X^2+1 X^2 X+1 X^2 X+1 X^2+X X^3+X^2+X X^3+X^2+1 X^3+X+1  0 X^3+X^2  1 X^3  X X^3+X^2+X+1  0 X^3+X  1  1  0
 0  0  0  1  1 X^2 X^2+1  1 X^2+X+1 X^3+X X^2+1 X^2+1 X^2 X^3+X^2+1 X^3+X^2 X^3+1  0 X^2 X^3+X^2+X+1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1 X^2+X+1 X^3+X^2+X  0  1  X X^2+X+1 X^3+X^2+X+1 X^3+X X^3+1 X+1  1 X^3+X^2+X+1 X+1 X^3 X^2 X^3+X^2+X X+1 X^3+X^2  1  1 X^2+X+1  1 X^3+X X^2  X X^2+X X^3+X^2 X^3+X  0
 0  0  0  0 X^3+X^2  0 X^3+X^2  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2  0 X^3+X^2  0  0  0 X^2  0 X^2 X^3 X^3+X^2 X^3 X^3+X^2  0  0 X^2 X^3+X^2 X^3  0  0  0 X^3+X^2

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+106x^43+809x^44+2978x^45+6272x^46+11550x^47+20141x^48+29564x^49+38031x^50+42432x^51+37980x^52+31174x^53+20793x^54+10986x^55+5444x^56+2356x^57+965x^58+394x^59+101x^60+36x^61+15x^62+4x^63+2x^64+4x^65+4x^66+2x^68

The gray image is a linear code over GF(2) with n=408, k=18 and d=172.
This code was found by Heurico 1.16 in 391 seconds.