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

generates a code of length 48 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+42x^45+89x^46+281x^48+64x^50+20x^53+6x^54+6x^56+2x^61+1x^62

The gray image is a code over GF(2) with n=384, k=9 and d=180.
This code was found by Heurico 1.16 in 12.2 seconds.