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

generates a code of length 48 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+206x^44+232x^46+256x^47+679x^48+256x^49+208x^50+194x^52+8x^54+7x^56+1x^88

The gray image is a code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 4 seconds.