The generator matrix

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

generates a code of length 52 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+328x^50+120x^51+210x^52+48x^53+248x^54+24x^55+43x^56+1x^68+1x^76

The gray image is a code over GF(2) with n=416, k=10 and d=200.
This code was found by Heurico 1.16 in 8.39 seconds.