The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+560x^46+634x^47+821x^48+642x^49+492x^50+286x^51+272x^52+150x^53+163x^54+16x^55+56x^56+2x^60+1x^62

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 39.5 seconds.