The generator matrix

 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  1  1  X  1  1  1  1  1  1 2X+2  X  1  1  1  1  1  1  2 2X  X  X
 0  X  0  X 2X  0 3X  X  2 X+2  2 3X+2 2X+2  2 X+2 X+2  0 2X 3X X+2  2  X 3X+2  X  2  0 X+2  2  X 3X 2X+2 X+2  0 X+2 3X 3X+2 2X 2X 3X 3X+2  0 2X+2 3X 2X+2  2  X 2X 2X+2
 0  0  X  X  2 X+2 X+2  2  2 2X  X 3X  0 X+2 3X+2 2X+2  0 3X+2 X+2 X+2 X+2 3X  X 2X+2 3X 3X 3X+2 2X  0 3X+2  2  2  2 2X 3X  0  X  X 2X X+2  X  X  0 2X  X  X 3X X+2
 0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X 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+103x^44+192x^45+254x^46+280x^47+484x^48+264x^49+204x^50+112x^51+63x^52+40x^53+30x^54+8x^55+12x^56+1x^80

The gray image is a code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 0.125 seconds.