The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+616x^47+1804x^48+3452x^49+5514x^50+7660x^51+8688x^52+10134x^53+8738x^54+8068x^55+5355x^56+2964x^57+1504x^58+672x^59+230x^60+90x^61+26x^62+8x^63+10x^64+2x^66

The gray image is a code over GF(2) with n=424, k=16 and d=188.
This code was found by Heurico 1.16 in 30.6 seconds.