The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+413x^46+1900x^47+3312x^48+5768x^49+7552x^50+8976x^51+9910x^52+9254x^53+7236x^54+5752x^55+3058x^56+1552x^57+537x^58+172x^59+82x^60+34x^61+13x^62+13x^64+1x^66

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 28.6 seconds.