The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X^3+X  1  1  1  1 X^2 X^3+X^2+X  1  X  1  1  1  X  1  1 X^2 X^3  X X^3+X X^3 X^3  1  1 X^3  1  X  1  1  1  1  1  1  1  X  1  1  1  0 X^2+X X^3+X^2+X X^3+X^2  1
 0  1  1 X^2+X  1 X^2+X+1 X^2 X^3+1  1 X+1 X^3+X^2+X  1  1  0 X^3+X^2+1 X^3 X^3+1  1  1 X^3+X^2+1  1 X^2+X+1 X^3+X^2  X  1  X X+1  1  1  1  1  1  1 X^2+X X^3+X^2+X+1  1 X+1  1 X^2+X X^3+1  X X^3 X^3+X^2 X^2+X+1 X^3+1 X^2  1 X^3+X X^2 X^3+X^2  1  1  1  X
 0  0  X  0 X^3+X  X X^3+X X^3  0 X^3 X^3+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2  X  X X^3+X^2  0 X^3+X^2+X  0 X^3+X^2 X^3+X^2+X  X X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3+X^2 X^3+X^2+X X^3 X^3+X X^3+X X^3+X X^3  0 X^3+X  X X^2+X X^3+X^2 X^2+X  X X^2 X^3+X^2 X^2  X X^2  X X^3  X
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  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+166x^50+588x^51+532x^52+544x^53+619x^54+632x^55+386x^56+240x^57+165x^58+124x^59+40x^60+48x^61+8x^62+1x^64+1x^70+1x^74

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 0.282 seconds.