The generator matrix

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

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+183x^44+228x^45+674x^46+680x^47+1177x^48+1144x^49+1668x^50+1548x^51+1868x^52+1504x^53+1724x^54+1180x^55+1144x^56+680x^57+476x^58+164x^59+201x^60+28x^61+58x^62+12x^63+30x^64+8x^66+4x^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 9.11 seconds.