The generator matrix

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

generates a code of length 49 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+366x^43+1728x^44+3302x^45+5227x^46+7318x^47+9894x^48+10254x^49+9418x^50+7682x^51+5342x^52+2762x^53+1463x^54+490x^55+185x^56+66x^57+20x^58+16x^59+2x^64

The gray image is a code over GF(2) with n=392, k=16 and d=172.
This code was found by Heurico 1.16 in 23.9 seconds.