The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^49+219x^50+336x^51+304x^52+250x^53+274x^54+266x^55+212x^56+72x^57+11x^58+20x^59+2x^61+2x^63+2x^64+1x^80

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 0.156 seconds.