The generator matrix

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

generates a code of length 50 over Z2[X]/(X^4) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+592x^47+536x^48+984x^49+467x^50+548x^51+300x^52+392x^53+59x^54+96x^55+42x^56+64x^57+1x^58+12x^59+1x^62+1x^64

The gray image is a linear code over GF(2) with n=400, k=12 and d=188.
This code was found by Heurico 1.16 in 2.2 seconds.