The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+604x^49+612x^50+884x^51+480x^52+548x^53+304x^54+296x^55+92x^56+180x^57+44x^58+36x^59+12x^61+3x^64

The gray image is a code over GF(2) with n=416, k=12 and d=196.
This code was found by Heurico 1.16 in 5.83 seconds.