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

generates a code of length 52 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+209x^44+1200x^45+3117x^46+6510x^47+12374x^48+20102x^49+29296x^50+37602x^51+40762x^52+37762x^53+30180x^54+20614x^55+11872x^56+6070x^57+2806x^58+1046x^59+373x^60+134x^61+71x^62+20x^63+9x^64+12x^65+2x^66

The gray image is a code over GF(2) with n=416, k=18 and d=176.
This code was found by Heurico 1.16 in 428 seconds.