The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  2  1  1  1  X  1  2  1  1  1 2X  1 3X  1  1 3X+2 2X+2  1 X+2 X+2  0  1  1  1  1  X  2  X  X 2X  1 X+2 2X+2 3X  2  X  1  1  X  1
 0  1 X+1 X+2 2X+3  1 3X+1  0  1 2X+1 X+2  1  2  1 X+1 3X+2  3  1 2X+2  1 3X+3  0 X+1  1 3X  1  3  3  1  1 2X  1  1  1  1 X+2 3X 3X+3 X+2  1  1  1  X 3X+2  1  1  1  1  1  1 2X+1 2X  0
 0  0 2X+2  0  0 2X  0 2X+2  2  2 2X+2  2  2 2X  2  0  0 2X+2 2X+2 2X+2  2 2X 2X 2X  2 2X+2 2X+2 2X+2  0 2X+2  2 2X+2 2X  2 2X+2  2  2 2X+2  2  0  2 2X+2  0  0 2X 2X+2 2X  2  0  0 2X  2  0
 0  0  0  2 2X 2X+2 2X+2  2  2 2X+2 2X 2X  2  0 2X+2  0 2X+2 2X 2X 2X+2  0  2 2X  2  2  2  0 2X+2 2X 2X  0 2X+2  2  0 2X 2X+2 2X  2  0  2 2X  0 2X+2 2X 2X  2  0  2  0 2X+2  2  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+30x^48+240x^49+417x^50+550x^51+627x^52+528x^53+551x^54+488x^55+343x^56+212x^57+47x^58+16x^59+21x^60+8x^61+9x^62+4x^65+2x^67+2x^72

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 0.234 seconds.