The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1 X^3+X^2  1  X  1  1  1  1  1  0  1 X^3  1  1 X^3+X^2  1 X^3+X X^2  1  1  1 X^2+X  1  0 X^2+X  1  1 X^3+X  1 X^3+X X^2+X  1 X^3+X^2 X^3+X  1  1 X^3 X^3  0 X^3+X^2 X^3+X X^3+X^2  1  1  0  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X^2+1 X^3+X^2  1  X  1 X^3+1 X^2+X+1  1 X+1  0  1 X^3  1 X+1 X^3+X^2  1 X^3+X^2+1  1  1 X^3+X^2+X  1 X^3  1  X  1  1  1 X^3+X^2+X+1  1 X^2+X  1  1 X^2  1  1 X^3+X^2+X X^3+X  1  1  1  1  1  1 X^2 X^2+X  1 X^3+1 X+1
 0  0 X^2  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^2 X^3 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^3 X^3  0 X^3+X^2 X^2  0 X^3  0 X^2 X^3+X^2 X^2  0  0 X^2 X^3 X^2  0
 0  0  0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^2 X^2  0 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^2 X^3 X^3  0  0  0  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^2 X^3 X^3  0 X^2 X^3+X^2 X^2 X^2  0 X^3+X^2 X^2  0  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3+X^2 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+382x^50+192x^51+758x^52+320x^53+826x^54+320x^55+734x^56+192x^57+346x^58+9x^60+6x^62+8x^66+1x^76+1x^80

The gray image is a linear code over GF(2) with n=432, k=12 and d=200.
This code was found by Heurico 1.16 in 131 seconds.