The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+682x^49+570x^50+752x^51+596x^52+496x^53+290x^54+304x^55+130x^56+226x^57+11x^58+32x^59+4x^61+1x^64+1x^66

The gray image is a code over GF(2) with n=416, k=12 and d=196.
This code was found by Heurico 1.16 in 81.5 seconds.