The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  0  1  1  1  X  1  1 2X+2  1  1 2X  X  1  X  1  0  1  2  1  1 2X 2X 2X 2X  1
 0  X  0 3X+2  2 X+2 2X+2  X  0 X+2 2X X+2 3X  2  2  X  0 X+2 3X+2  X  2 2X 2X 3X  X  X 2X+2  0  X X+2  X 2X X+2 2X 3X+2  X 2X+2 X+2  X X+2  2  0  0  X 3X  0  2  X  X  X  X  2 3X
 0  0 2X+2  0  2  0 2X  0  2  2 2X 2X+2 2X+2 2X+2  0  2  0 2X+2  2  2 2X 2X+2 2X+2  0 2X  0 2X+2  0 2X  2  2  2 2X  0 2X+2  0  0 2X 2X+2  2 2X+2 2X  0 2X+2 2X 2X+2 2X+2  2 2X+2 2X+2  0  2 2X
 0  0  0 2X+2  0 2X 2X  2  2  2  2  0  0  2 2X+2  2 2X 2X+2  0  0  2 2X 2X+2 2X  2  2  2 2X 2X  2 2X  0  0  2  0 2X 2X  2  0  2 2X+2 2X+2 2X+2  2 2X+2  0  0 2X+2  2  0 2X+2  2  2
 0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X 2X 2X  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+263x^48+64x^49+576x^50+176x^51+770x^52+528x^53+706x^54+208x^55+478x^56+48x^57+174x^58+74x^60+14x^62+9x^64+2x^66+4x^68+1x^80

The gray image is a code over GF(2) with n=424, k=12 and d=192.
This code was found by Heurico 1.16 in 120 seconds.