The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+60x^41+263x^42+762x^43+1642x^44+2616x^45+3853x^46+5844x^47+7600x^48+9702x^49+11980x^50+13618x^51+14445x^52+13752x^53+12327x^54+10338x^55+8123x^56+5776x^57+3680x^58+2024x^59+1187x^60+816x^61+336x^62+178x^63+88x^64+46x^65+9x^66+4x^67+2x^68

The gray image is a code over GF(2) with n=208, k=17 and d=82.
This code was found by Heurico 1.13 in 163 seconds.