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  1  1  1  1  0  X  X  2  X  X  X  1  2  X  1  X  0  2  1  X  1  X
 0  X  0  0  0  0  0  0  2  2  X X+2  X  0  0  2 X+2 X+2  X  X  X  0  X  X  2 X+2  X X+2  2 X+2  X  2  2  X  0  X  0  2  0  0  2  X  2 X+2  2  X  X  X X+2  2  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  2 X+2 X+2 X+2  X X+2 X+2  X  2 X+2  X  2  X  X  X  2  X  X  0  X  2  0  X  2  2  X X+2  2  X X+2  X  2 X+2  0  0  X  X X+2  X X+2
 0  0  0  X  0  0  2 X+2  X  X  X  X  2 X+2  X  2  2  0  2  2  2  2  X X+2  2  X X+2  X  X X+2  2  X  X  0  X  0  X  0  X X+2  0  X  X X+2  0  X  2 X+2 X+2 X+2 X+2  2
 0  0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  X  X  0  2  X  0 X+2 X+2 X+2  X  0 X+2 X+2  2  0  0  2  X  2 X+2  0  2 X+2  2  X  0  0  0  X  2 X+2  2  0  2  X  X X+2  0  2
 0  0  0  0  0  X  X  2 X+2  X X+2  2  X  X  0  X  0 X+2 X+2  0  X  2 X+2  X  X  2  0  0  2  X  2 X+2  0  2  X  0  0  2  X X+2 X+2  0  0 X+2 X+2  2  2 X+2  0  0  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+90x^43+171x^44+178x^45+259x^46+344x^47+498x^48+678x^49+663x^50+816x^51+941x^52+776x^53+713x^54+590x^55+425x^56+316x^57+229x^58+180x^59+123x^60+94x^61+48x^62+26x^63+16x^64+6x^65+8x^66+2x^67+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 42.8 seconds.