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

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+9x^50+40x^51+34x^52+184x^53+490x^54+184x^55+29x^56+40x^57+12x^58+1x^106

The gray image is a linear code over GF(2) with n=432, k=10 and d=200.
This code was found by Heurico 1.16 in 0.141 seconds.