The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+204x^44+260x^45+610x^46+732x^47+1052x^48+1284x^49+1472x^50+1784x^51+1486x^52+1868x^53+1738x^54+1344x^55+824x^56+652x^57+522x^58+232x^59+172x^60+32x^61+68x^62+4x^63+35x^64+6x^66+2x^68

The gray image is a code over GF(2) with n=208, k=14 and d=88.
This code was found by Heurico 1.16 in 9.52 seconds.