The generator matrix

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

generates a code of length 48 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+70x^42+56x^43+224x^44+428x^45+352x^46+768x^47+350x^48+872x^49+250x^50+360x^51+166x^52+76x^53+78x^54+21x^56+16x^58+5x^60+2x^62+1x^68

The gray image is a code over GF(2) with n=384, k=12 and d=168.
This code was found by Heurico 1.16 in 0.344 seconds.