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

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+17x^48+28x^49+30x^50+104x^51+672x^52+96x^53+31x^54+24x^55+14x^56+4x^57+2x^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 0.109 seconds.