The generator matrix

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

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+380x^46+892x^47+1154x^48+1432x^49+1207x^50+1048x^51+712x^52+640x^53+351x^54+172x^55+140x^56+40x^57+13x^58+8x^60+1x^62+1x^64

The gray image is a linear code over GF(2) with n=400, k=13 and d=184.
This code was found by Heurico 1.16 in 1.17 seconds.