The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+200x^43+786x^44+1778x^45+1955x^46+2576x^47+2195x^48+2656x^49+1601x^50+1350x^51+742x^52+320x^53+121x^54+64x^55+16x^56+12x^57+3x^58+2x^59+4x^60+2x^61

The gray image is a code over GF(2) with n=384, k=14 and d=172.
This code was found by Heurico 1.16 in 1.98 seconds.