The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+168x^45+1055x^46+3002x^47+6655x^48+11736x^49+20614x^50+28886x^51+38690x^52+40008x^53+38686x^54+29732x^55+21288x^56+11626x^57+5916x^58+2432x^59+1054x^60+318x^61+155x^62+74x^63+24x^64+14x^65+6x^66+2x^67+2x^69

The gray image is a code over GF(2) with n=424, k=18 and d=180.
This code was found by Heurico 1.16 in 454 seconds.