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

generates a code of length 53 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+164x^49+60x^50+232x^51+336x^52+580x^53+309x^54+160x^55+45x^56+60x^57+14x^58+56x^59+1x^60+28x^61+1x^62+1x^92

The gray image is a code over GF(2) with n=424, k=11 and d=196.
This code was found by Heurico 1.16 in 105 seconds.