The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  1  1  1  1  1  X  1  X  X  X  X  X  X  X  X  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2 X^2 X^2+2  0 X^2 X^2  0  2 X^2 X^2+2  0 X^2+2 X^2  0 X^2 X^2+2  2 X^2+2  2  0  2 X^2+2  2  0  2 X^2  0 X^2+2  2  0 X^2+2 X^2  0  2  0 X^2
 0  0 X^2+2 X^2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  0 X^2+2 X^2  0 X^2 X^2  0 X^2+2  2 X^2+2  0 X^2 X^2  0  2 X^2+2  2 X^2  0  2 X^2+2 X^2  2  0  0 X^2 X^2+2  2  2 X^2+2 X^2+2  2  0 X^2 X^2+2  0  0 X^2 X^2+2 X^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+7x^50+34x^51+175x^52+26x^53+8x^54+2x^55+2x^69+1x^70

The gray image is a code over GF(2) with n=416, k=8 and d=200.
This code was found by Heurico 1.16 in 0.062 seconds.