The generator matrix

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

generates a code of length 47 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+501x^44+696x^45+908x^46+416x^47+598x^48+336x^49+344x^50+96x^51+108x^52+56x^53+20x^54+15x^56+1x^60

The gray image is a code over GF(2) with n=376, k=12 and d=176.
This code was found by Heurico 1.16 in 46.7 seconds.