The generator matrix

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

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+90x^50+600x^51+532x^52+808x^53+499x^54+552x^55+274x^56+340x^57+160x^58+168x^59+40x^60+28x^61+1x^62+2x^66+1x^72

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 0.734 seconds.