The generator matrix

 1  0  0  0  1  1  1  1  1  0  2  X  0  1  1  2  0  X  1  1  1  2 X+2  0  1  1  1  0  1  X  1 X+2 X+2 X+2  1  1  1  1 X+2  2  1  0  1  1  1  0 X+2  0  1  1  X  1
 0  1  0  0  X  1  2 X+2  3  1  1  1  0 X+1 X+3  1 X+2  1 X+3  X X+2  X  1  2  3 X+2  2  1  1  0  X  1 X+2  2 X+3  0 X+2 X+3  0  1 X+1  1 X+1  2  X  1  1  X  X  1  1  0
 0  0  1  0  0  0  1  3  1 X+3  2 X+3  1 X+2 X+1  X  1  3 X+3  3  1  1  0 X+2  X  0 X+2  3 X+3  1 X+2  3  1  2 X+2  3 X+3 X+3  1  X  0  3  X X+3  0  3 X+1  2  0  1 X+2  0
 0  0  0  1  1 X+3 X+1  0 X+2 X+2  3  3 X+1  X  3  2  0 X+1 X+1 X+2  3  3 X+3  1 X+1  2 X+3  2  2  2  X  1  X  1  2  1 X+2 X+2  1 X+1 X+3  X X+2  0  2  X  3  1  1  1  2  0
 0  0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  0  0  2  2  0  2  2  0  2  0  2  2  2  2  2  2  2  2  2  0  0  2  0  0  0  0  0  2  2  0  2  0  0  2  0  0
 0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  2  0  0  2  0  2  0  2  0  2  2  0  0  2  0  0  0  2  0  2  0  2  0  0  0  2  0  0  2  0  0  0  2  0  2  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+86x^44+326x^45+560x^46+892x^47+1093x^48+1356x^49+1318x^50+1862x^51+1632x^52+1708x^53+1347x^54+1416x^55+1000x^56+762x^57+446x^58+294x^59+144x^60+66x^61+36x^62+16x^63+10x^64+6x^65+4x^66+2x^68+1x^70

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 8.35 seconds.