The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+332x^43+1698x^44+3258x^45+5407x^46+7588x^47+9456x^48+10162x^49+9816x^50+7408x^51+5287x^52+2936x^53+1415x^54+484x^55+178x^56+74x^57+18x^58+12x^59+1x^60+2x^61+3x^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 24.8 seconds.