The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+49x^52+8x^54+1x^56+4x^58+1x^60

The gray image is a code over GF(2) with n=416, k=6 and d=208.
This code was found by Heurico 1.16 in 0.079 seconds.