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 2X+2  0  0  0  2 2X+2  2  0 2X  2 2X+2 2X 2X  2  2  2  0 2X+2 2X 2X 2X+2  2 2X 2X  2  0  0  0 2X+2  2  0 2X+2 2X+2 2X  0 2X+2 2X  0 2X+2  0 2X+2 2X+2 2X+2 2X  0 2X 2X
 0  0 2X+2  0  2  2 2X+2  0  0 2X+2 2X+2 2X  0  2  2 2X 2X+2 2X 2X+2 2X  2  0 2X  2  0  2 2X  2  2  0 2X 2X  2 2X 2X+2 2X  2 2X 2X+2  2 2X+2  0 2X+2 2X  0  0 2X+2  0
 0  0  0 2X+2  2  0 2X+2  2 2X  2  2  0  2 2X 2X 2X+2 2X+2 2X 2X 2X+2  2 2X+2  0  0  0  2 2X+2 2X+2 2X  2 2X  0 2X  2  0  2  2  0  2  0 2X+2 2X  0 2X 2X+2  2 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+21x^44+32x^45+28x^46+32x^47+796x^48+32x^49+28x^50+32x^51+21x^52+1x^96

The gray image is a code over GF(2) with n=384, k=10 and d=176.
This code was found by Heurico 1.16 in 0.079 seconds.