The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1
 0  X  2 3X+2  0 3X+2  2 3X  0 3X+2 3X  2 2X X+2 2X+2 3X  0 3X+2  2 3X  0 3X+2  2 3X  0 3X  2 3X+2 2X X+2 2X+2  X  0 3X+2  2 3X 2X X+2 2X+2  X 2X+2 X+2 2X  X 2X 2X  0 2X+2 3X+2  X  0  0
 0  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0  0 2X 2X  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X 2X  0  0  0  0  0 2X  0
 0  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  0  0  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X  0 2X  0  0  0  0 2X  0  0 2X 2X  0 2X 2X 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+15x^48+80x^49+32x^50+48x^51+676x^52+80x^53+27x^54+16x^55+12x^56+32x^57+4x^58+1x^102

The gray image is a code over GF(2) with n=416, k=10 and d=192.
This code was found by Heurico 1.16 in 0.125 seconds.