The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+640x^50+624x^51+946x^52+304x^53+504x^54+368x^55+369x^56+80x^57+152x^58+32x^59+74x^60+1x^64+1x^72

The gray image is a code over GF(2) with n=424, k=12 and d=200.
This code was found by Heurico 1.16 in 57 seconds.