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  X  2  X X^2  X  X  0  X X^2+2  X X^2  X  X  0  X  X  X  X  X  X
 0  X  0 X^2+X+2  0 X^2+X  0 X+2 X^2 X^2+X X^2+2  X X^2 X^2+X+2 X^2+2 X+2  2 X^2+X  2  X  2 X^2+X+2  2 X+2 X^2+2 X^2+X+2 X^2 X+2 X^2+2 X^2+X X^2  X X^2+X  X X+2  X  2 X^2+X+2  X  X  X  0  2 X^2 X^2+2  0 X^2 X^2+2  0  0 X^2+X X+2
 0  0 X^2+2 X^2  2 X^2+2 X^2  2 X^2  0  0 X^2 X^2+2  2  2 X^2+2  2  2 X^2 X^2+2  0  0 X^2+2 X^2 X^2+2 X^2+2  2  0 X^2 X^2  0  2  0 X^2  2 X^2+2 X^2 X^2  2 X^2  0 X^2 X^2+2 X^2  0 X^2 X^2+2  2  0  2  2  2

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+136x^50+96x^51+158x^52+40x^54+32x^55+30x^56+16x^58+2x^60+1x^64

The gray image is a code over GF(2) with n=416, k=9 and d=200.
This code was found by Heurico 1.16 in 0.11 seconds.