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 3X+2  1 3X  1  1  1  1  1  2
 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 2X+2  1  3  1 3X+1 3X X+2 X+3 3X  1
 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 3X+2 X+3  3 X+2 X+3 X+3 3X 3X+3  1 3X+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+622x^49+580x^50+878x^51+542x^52+492x^53+265x^54+376x^55+111x^56+114x^57+34x^58+74x^59+4x^61+1x^62+2x^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 266 seconds.