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  X  1  1 2X  X  X
 0  X  0 3X+2 2X+2 X+2  2  X  0 3X+2  2 3X 2X  X  2 X+2  X  0  2 X+2 X+2 2X 2X+2 3X 3X  0 X+2  0 X+2  2  2 3X 3X 2X 2X 2X+2 3X+2 2X+2 3X+2 X+2 2X+2  0 2X 3X+2  2 3X+2 3X+2  X  X  X X+2 X+2
 0  0  2  0  2 2X+2  0 2X+2 2X 2X 2X 2X 2X+2  2 2X+2  2 2X+2  0  0 2X+2 2X 2X+2 2X+2 2X  2 2X  2  2  0  2 2X  0  2 2X  2  2 2X+2 2X  0  0  0 2X+2 2X  2  2  2  0  0 2X 2X+2 2X+2 2X+2
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0  0 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+54x^49+112x^50+214x^51+284x^52+192x^53+112x^54+40x^55+2x^56+10x^57+2x^59+1x^96

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 0.156 seconds.