The generator matrix

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

generates a code of length 50 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+180x^46+56x^47+268x^48+336x^49+456x^50+320x^51+202x^52+48x^53+92x^54+8x^55+71x^56+8x^58+1x^60+1x^84

The gray image is a linear code over GF(2) with n=400, k=11 and d=184.
This code was found by Heurico 1.16 in 1.49 seconds.