The generator matrix

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

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+126x^48+128x^49+459x^50+368x^51+724x^52+544x^53+693x^54+384x^55+422x^56+96x^57+93x^58+16x^59+34x^60+3x^62+1x^64+1x^68+1x^72+1x^76+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 0.234 seconds.