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  1  1  1  1  1  1  1  1  X  1  1
 0  X  2 3X+2  0 3X+2  2 3X  0 3X+2 3X  2 2X X+2 2X+2 3X  0 3X+2  2 3X  0 3X+2  2 3X  0 3X+2  2 3X 2X X+2 2X+2  X  0 3X+2  2 3X 2X X+2 2X+2  X 2X X+2 2X+2  X 2X 2X X+2 3X+2  0 2X+2  2 3X+2 X+2  0
 0  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0 2X  0  0  0 2X 2X 2X  0  0  0  0  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X  0  0  0 2X 2X 2X  0
 0  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0  0 2X  0  0 2X  0 2X 2X 2X  0  0  0  0 2X  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+9x^50+40x^51+34x^52+184x^53+490x^54+184x^55+29x^56+40x^57+12x^58+1x^106

The gray image is a code over GF(2) with n=432, k=10 and d=200.
This code was found by Heurico 1.16 in 0.125 seconds.