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  0  2  0  1  0  X  1  0  1  1  X  1  0  0  0  X  1  1  0  2  0  1
 0  X  0  0  0  0  0  0  0 X+2  X  X  X  X  2  2  0  X  2 X+2  X  0  2  2  X  0  X X+2  2 X+2  2  X  X  0  2  2  0  0  X  0 X+2 X+2  X  X  X  0  2  0  X  X  2  0
 0  0  X  0  0  0  X X+2  X  2  X X+2  0  0  X X+2 X+2 X+2  0  2  X X+2 X+2 X+2  X  2 X+2  X X+2  0  X X+2 X+2  0  2  0  X  X  2  2 X+2  X X+2  X X+2 X+2  0 X+2  X  2  0  2
 0  0  0  X  0  X  X  X  0 X+2  2  X X+2  0  X X+2  0  0 X+2  X  2  X  0  2  2  0  X  X  0  X  2  0  2  0  X  0 X+2  X  X  2  X  2  0 X+2  2  2  X  0 X+2  0  X  X
 0  0  0  0  X  X  0  X X+2  X  0  X  2 X+2 X+2  0  X X+2  2  2  0 X+2  X  0  0  X X+2  0  2 X+2  0  0  X  2  0  X X+2 X+2  2  0  2  2 X+2 X+2 X+2  2  0  X  X  0  X  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  2  2  2  0  0  2  2  2  2  2  0  2  2  2  2  2  0  0  0  2  2  2  0  0  2  2  0  0
 0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  2  2  0  2  0  2  2  0  2  0  2  2  0  2  0  0  0  2  2  0  0  2  0  0  0  0  0  0  0  0  2  2  0  0  2  2  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+80x^43+218x^44+218x^45+90x^46+466x^47+385x^48+956x^49+149x^50+1360x^51+428x^52+1386x^53+132x^54+946x^55+330x^56+438x^57+90x^58+182x^59+151x^60+68x^61+42x^62+36x^63+20x^64+6x^65+9x^66+2x^67+2x^68+1x^76

The gray image is a code over GF(2) with n=208, k=13 and d=86.
This code was found by Heurico 1.16 in 83.3 seconds.