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

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+23x^50+32x^51+68x^52+222x^53+339x^54+236x^55+53x^56+16x^57+19x^58+4x^59+6x^60+2x^61+2x^62+1x^102

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 0.14 seconds.