The generator matrix

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

generates a code of length 48 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+192x^46+638x^48+192x^50+1x^96

The gray image is a code over GF(2) with n=384, k=10 and d=184.
This code was found by Heurico 1.16 in 10.9 seconds.