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 2X+2  0  0  0  2 2X+2  2  0  0  0 2X  2  2  2 2X+2 2X+2 2X  2 2X 2X 2X 2X+2 2X+2 2X+2  0 2X+2  0 2X+2 2X+2 2X  0 2X 2X 2X+2  2  0  0 2X+2  2 2X 2X  2 2X 2X 2X+2  2 2X 2X 2X  2  2 2X+2 2X
 0  0 2X+2  0  2  2 2X+2  0  0  0  2  2 2X+2 2X 2X+2 2X 2X+2 2X+2 2X+2 2X+2 2X  0 2X 2X  0 2X  2  2  0  2  2 2X  0 2X+2  2 2X 2X  2  2  0  0  2  0 2X  2 2X+2 2X 2X+2 2X  0  2  2 2X  0
 0  0  0 2X+2  2  0 2X+2  2 2X  2 2X+2  0  0  2 2X+2 2X 2X  0  2  2 2X  2 2X+2  0  2  0 2X+2 2X 2X  0 2X+2 2X+2 2X+2 2X+2 2X  0 2X  0  2 2X+2 2X  2 2X 2X+2 2X  2 2X+2 2X  0  0 2X+2  0  2  2

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

Homogenous weight enumerator: w(x)=1x^0+21x^50+26x^51+29x^52+104x^53+670x^54+100x^55+23x^56+24x^57+20x^58+2x^59+3x^60+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 0.109 seconds.