The generator matrix

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

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+24x^48+124x^49+147x^50+186x^51+429x^52+330x^53+403x^54+144x^55+100x^56+52x^57+19x^58+54x^59+21x^60+6x^61+6x^62+1x^64+1x^86

The gray image is a code over GF(2) with n=424, k=11 and d=192.
This code was found by Heurico 1.16 in 0.235 seconds.