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

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

Homogenous weight enumerator: w(x)=1x^0+211x^44+296x^46+256x^47+564x^48+256x^49+240x^50+201x^52+8x^54+14x^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 25.5 seconds.