The generator matrix

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

generates a code of length 52 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+380x^46+1922x^47+3640x^48+5540x^49+6925x^50+9778x^51+9124x^52+9954x^53+7282x^54+5678x^55+2921x^56+1442x^57+593x^58+214x^59+86x^60+22x^61+20x^62+8x^63+4x^64+2x^65

The gray image is a code over GF(2) with n=416, k=16 and d=184.
This code was found by Heurico 1.16 in 27.3 seconds.