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  X  1 X^2  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2  0 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3 X^2  0 X^3 X^3 X^3+X^2 X^2 X^2  0 X^3  0 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2  0 X^3  0
 0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3  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  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0 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+37x^50+91x^52+64x^53+647x^54+64x^55+86x^56+19x^58+13x^60+1x^62+1x^104

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.