The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+288x^43+652x^44+1362x^45+2039x^46+3138x^47+3875x^48+5180x^49+5818x^50+6882x^51+6747x^52+6948x^53+6140x^54+5408x^55+4106x^56+3032x^57+1692x^58+1140x^59+528x^60+330x^61+113x^62+70x^63+22x^64+12x^65+6x^66+2x^67+5x^68

The gray image is a code over GF(2) with n=208, k=16 and d=86.
This code was found by Heurico 1.13 in 45.9 seconds.