The generator matrix

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

generates a code of length 49 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+548x^46+708x^47+714x^48+684x^49+440x^50+356x^51+277x^52+164x^53+132x^54+8x^55+54x^56+8x^58+1x^60+1x^64

The gray image is a code over GF(2) with n=392, k=12 and d=184.
This code was found by Heurico 1.16 in 0.25 seconds.