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

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+284x^49+353x^50+376x^51+171x^52+304x^53+263x^54+188x^55+35x^56+52x^57+3x^58+8x^59+1x^60+4x^62+4x^63+1x^78

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 0.187 seconds.