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

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+57x^44+64x^46+781x^48+64x^50+54x^52+2x^56+1x^92

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 0.11 seconds.