The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+322x^47+942x^48+1530x^49+2107x^50+2294x^51+2448x^52+2166x^53+1861x^54+1352x^55+783x^56+302x^57+137x^58+72x^59+31x^60+18x^61+7x^62+6x^63+2x^64+2x^67+1x^68

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 2.03 seconds.