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  2  1  1  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X X+2  0 2X+2 3X 2X X+2  2 3X 3X+2  0 3X 2X+2  0 3X 2X+2 X+2  0 X+2 2X+2 3X 2X 3X+2  2  X  0 X+2 2X+2 3X+2 2X  X  2  X 3X+2 2X  2  X 2X+2 2X 2X+2  0
 0  0 2X  0  0  0 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0
 0  0  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0 2X  0  0  0  0 2X  0 2X  0 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X
 0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X  0  0  0  0  0  0 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X  0 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+16x^44+52x^45+27x^46+280x^47+295x^48+248x^49+32x^50+56x^51+8x^52+4x^53+4x^54+1x^94

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 0.078 seconds.