The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  1  1  1  1  1  X  1 2X  X  1 2X+2  1  1  0  1  X  1  2  1  1  1  1 2X  1
 0  X  0  X 2X  0 3X+2 X+2  0 2X 3X 3X  0  2 X+2  X  2 3X+2 X+2 2X 2X X+2  X 3X+2 3X 3X+2 2X+2  2 3X X+2 3X  X X+2  2 2X+2 X+2  2  X 3X+2 2X+2  0 2X  X  0  X 2X+2  X 2X
 0  0  X  X  0 X+2 3X+2 2X 2X+2 X+2 X+2 2X+2  2  X 2X+2  X X+2 3X  X 3X  2  2  2  0 2X  2  X  0 3X+2  X 3X+2 X+2 2X 3X  X 2X+2 2X 2X 3X 3X+2 3X+2  X 2X+2  X 2X+2  X  2  X
 0  0  0 2X+2  2 2X+2 2X 2X+2 2X+2  0 2X+2  2  0  2  0 2X 2X+2  2 2X 2X+2 2X  0  2 2X 2X+2 2X 2X  2  0  0 2X  2 2X+2  0 2X+2  2 2X+2  0 2X+2  2  2 2X 2X+2  2 2X  0 2X 2X

generates a code of length 48 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+104x^43+236x^44+296x^45+428x^46+780x^47+573x^48+760x^49+310x^50+252x^51+170x^52+64x^53+40x^54+44x^55+26x^56+6x^58+4x^59+1x^60+1x^76

The gray image is a code over GF(2) with n=384, k=12 and d=172.
This code was found by Heurico 1.16 in 0.296 seconds.