The generator matrix

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

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+463x^48+128x^49+544x^50+384x^51+1084x^52+384x^53+544x^54+128x^55+414x^56+12x^60+8x^64+2x^80

The gray image is a code over GF(2) with n=416, k=12 and d=192.
This code was found by Heurico 1.16 in 1.52 seconds.