The generator matrix

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

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+632x^50+652x^51+734x^52+556x^53+556x^54+300x^55+296x^56+116x^57+144x^58+40x^59+54x^60+12x^62+3x^64

The gray image is a linear code over GF(2) with n=424, k=12 and d=200.
This code was found by Heurico 1.16 in 15.7 seconds.