The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+374x^48+882x^49+1609x^50+1926x^51+2502x^52+2320x^53+2345x^54+1678x^55+1372x^56+654x^57+400x^58+182x^59+74x^60+32x^61+19x^62+6x^63+5x^64+1x^66+2x^70

The gray image is a code over GF(2) with n=424, k=14 and d=192.
This code was found by Heurico 1.16 in 2.25 seconds.