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 X^3  1  1 X^3+X^2  1 X^3  1  1  1  0  1  1  1  1  1  1  X  1  0  1  X X^2  1  1
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^3+X^2+X X^3+X^2 X^2 X^2+X X^2+X  0 X^3 X^3+X X^3+X  0 X^2 X^3+X X^2+X X^2 X^3+X^2+X X^2 X^3+X^2  0 X^3 X^3+X^2+X  X X^3+X^2+X  X X^2  X  0  X X^3+X^2+X X^3  0 X^2 X^3+X^2+X  X X^2 X^3+X^2+X X^3+X^2+X X^3 X^3+X X^3+X^2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3  X X^3+X  0 X^2+X X^3+X^2+X X^3+X^2  0 X^3+X^2+X X^2+X X^3+X^2 X^3+X^2 X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X  X X^3+X X^3+X  X  X X^3+X X^3  0  0 X^2+X X^3+X^2+X X^3  0 X^2+X X^3 X^2 X^3+X  X  X X^3+X X^2  X  0 X^3
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 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+102x^46+166x^47+225x^48+362x^49+495x^50+292x^51+166x^52+88x^53+42x^54+30x^55+38x^56+22x^57+17x^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 0.141 seconds.