The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+454x^48+808x^49+1352x^50+1272x^51+1111x^52+1008x^53+788x^54+544x^55+483x^56+200x^57+128x^58+8x^59+29x^60+4x^62+2x^64

The gray image is a code over GF(2) with n=416, k=13 and d=192.
This code was found by Heurico 1.16 in 0.672 seconds.