The generator matrix

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

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+270x^49+360x^50+370x^51+259x^52+226x^53+274x^54+170x^55+43x^56+32x^57+17x^58+16x^59+4x^62+4x^63+1x^66+1x^76

The gray image is a code over GF(2) with n=416, k=11 and d=196.
This code was found by Heurico 1.16 in 2.31 seconds.