The generator matrix

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

generates a code of length 50 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+216x^43+1275x^44+3156x^45+6002x^46+10788x^47+14514x^48+18950x^49+20450x^50+20318x^51+14690x^52+10430x^53+5741x^54+2800x^55+1169x^56+370x^57+118x^58+38x^59+29x^60+6x^61+7x^62+2x^64+2x^66

The gray image is a linear code over GF(2) with n=400, k=17 and d=172.
This code was found by Heurico 1.16 in 98.8 seconds.