The generator matrix

 1  0  1  1 2X+2  1  1  1 3X+2  1  1  2  0  1  1  1  1  1  X  2  1  1  1 2X+2  1  2  1  1 X+2  2 X+2  X 3X+2 X+2 X+2  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1
 0  1  1 3X+2  1 3X+3 2X+2 2X+3  1 X+1  X  1  1 2X+2 X+1 2X  X  1  1  1  3  0  1  1 X+3  1  X X+3  1  1  1  1  1  1  1  3  0 X+2 3X+3  2 X+2 3X+3 2X+3 3X+2 2X X+2 2X  3 2X+3 X+2  0 2X+2
 0  0  X  0 3X  X 3X 2X  0 2X 3X X+2  2 X+2  2 2X+2 X+2 3X+2 3X X+2 3X  0 2X+2  2 2X  X  2 3X+2  0 2X 3X+2 X+2 3X 2X+2  2  2 3X+2 X+2  X  2  2 X+2  0 3X  X 2X  X 3X 3X+2  X 3X 3X
 0  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0  0 2X  0 2X  0  0  0 2X  0  0 2X  0 2X 2X 2X  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+162x^48+488x^49+794x^50+572x^51+326x^52+496x^53+606x^54+332x^55+146x^56+64x^57+70x^58+32x^59+4x^60+1x^64+2x^66

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 0.266 seconds.