The generator matrix

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

generates a code of length 50 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+216x^41+686x^42+1260x^43+2083x^44+2652x^45+4237x^46+4660x^47+6522x^48+6408x^49+7696x^50+6600x^51+6723x^52+5018x^53+4277x^54+2700x^55+1845x^56+878x^57+589x^58+260x^59+102x^60+58x^61+50x^62+8x^63+4x^64+2x^65+1x^66

The gray image is a code over GF(2) with n=200, k=16 and d=82.
This code was found by Heurico 1.13 in 43.4 seconds.