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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0  1  1  1  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^2+X  0 X^3+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X^2+X  0 X^3+X^2 X^3+X X^2+X  0 X^3+X^2 X^3+X^2+X X^3+X X^3+X  0 X^3+X^2 X^2+X  0 X^3+X^2  X X^3 X^3 X^2 X^2+X X^3+X^2+X X^2  X X^3+X  X X^3+X X^3+X  X X^3+X^2 X^2 X^3  0 X^3  0
 0  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3
 0  0  0 X^3  0  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  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+208x^46+158x^48+512x^49+352x^50+512x^51+64x^52+208x^54+32x^56+1x^96

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 0.734 seconds.