The generator matrix

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

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+280x^44+272x^45+660x^46+496x^47+713x^48+496x^49+648x^50+272x^51+232x^52+4x^54+9x^56+11x^60+1x^64+1x^68

The gray image is a code over GF(2) with n=384, k=12 and d=176.
This code was found by Heurico 1.16 in 3.44 seconds.