The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+484x^48+728x^49+1300x^50+1320x^51+1253x^52+998x^53+808x^54+468x^55+455x^56+152x^57+146x^58+36x^59+31x^60+10x^61+2x^66

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 0.578 seconds.