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

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+143x^50+96x^51+346x^52+304x^53+367x^54+292x^55+274x^56+48x^57+93x^58+24x^59+45x^60+5x^62+4x^63+5x^64+1x^92

The gray image is a code over GF(2) with n=432, k=11 and d=200.
This code was found by Heurico 1.16 in 0.172 seconds.