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 X^3  X  0  1  1 X^2  1 X^3  X  1  1
 0  X  0 X^3+X^2+X X^3 X^2+X  0  X X^2 X^3+X^2+X X^3+X^2  X X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X  0 X^3+X^2+X X^3+X^2  X  0 X^3+X X^3 X^3+X  0 X^2  X  X X^3+X^2+X X^3 X^3+X^2 X^2+X X^2+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X  0  X X^3 X^2 X^3  X  X X^3+X^2+X  X X^3+X  X  X X^3+X  X X^2+X  0 X^3
 0  0 X^3+X^2  0  0 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2  0 X^2 X^2 X^3 X^2 X^2  0 X^3 X^2 X^3 X^2 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2  0  0 X^3+X^2  0 X^3
 0  0  0 X^3+X^2 X^2 X^3+X^2 X^2  0  0  0 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3  0 X^3 X^2 X^3 X^2 X^2 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^2 X^3+X^2  0 X^3 X^2 X^2 X^3+X^2  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+224x^50+16x^51+274x^52+240x^53+554x^54+240x^55+262x^56+16x^57+206x^58+6x^60+6x^62+2x^66+1x^96

The gray image is a linear code over GF(2) with n=432, k=11 and d=200.
This code was found by Heurico 1.16 in 7.67 seconds.