The generator matrix

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

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+134x^47+192x^48+452x^49+330x^50+772x^51+545x^52+692x^53+288x^54+320x^55+117x^56+116x^57+50x^58+52x^59+7x^60+20x^61+4x^62+2x^63+1x^64+1x^80

The gray image is a code over GF(2) with n=416, k=12 and d=188.
This code was found by Heurico 1.16 in 0.328 seconds.