The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+540x^46+1884x^47+3572x^48+4824x^49+7690x^50+9246x^51+10385x^52+8918x^53+7805x^54+5036x^55+3239x^56+1468x^57+592x^58+206x^59+67x^60+22x^61+21x^62+12x^63+8x^64

The gray image is a code over GF(2) with n=416, k=16 and d=184.
This code was found by Heurico 1.16 in 27.3 seconds.