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

generates a code of length 52 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+79x^48+228x^49+269x^50+396x^51+322x^52+284x^53+188x^54+88x^55+66x^56+56x^57+20x^58+36x^59+12x^60+2x^62+1x^82

The gray image is a code over GF(2) with n=416, k=11 and d=192.
This code was found by Heurico 1.16 in 0.172 seconds.