The generator matrix

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

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+89x^50+236x^51+240x^52+336x^53+257x^54+360x^55+201x^56+208x^57+100x^58+12x^59+5x^60+1x^66+1x^76+1x^78

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 0.125 seconds.