The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+282x^47+991x^48+1542x^49+1989x^50+2318x^51+2689x^52+2122x^53+1834x^54+1178x^55+723x^56+408x^57+177x^58+76x^59+35x^60+2x^61+8x^62+1x^64+6x^65+2x^67

The gray image is a code over GF(2) with n=416, k=14 and d=188.
This code was found by Heurico 1.16 in 2.2 seconds.