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

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+52x^44+8x^45+96x^46+184x^47+369x^48+184x^49+66x^50+8x^51+35x^52+12x^54+6x^56+2x^58+1x^84

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 0.093 seconds.