The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+233x^48+1116x^49+1315x^50+2300x^51+2359x^52+2540x^53+1910x^54+2012x^55+1060x^56+888x^57+307x^58+192x^59+67x^60+32x^61+32x^62+8x^63+8x^64+4x^66

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 2.11 seconds.