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

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+46x^49+79x^50+160x^51+451x^52+170x^53+72x^54+36x^55+4x^56+4x^57+1x^102

The gray image is a code over GF(2) with n=416, k=10 and d=196.
This code was found by Heurico 1.16 in 0.078 seconds.