The generator matrix

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

generates a code of length 47 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+322x^41+1507x^42+3268x^43+5123x^44+7686x^45+9811x^46+10102x^47+10017x^48+7736x^49+5216x^50+2844x^51+1197x^52+470x^53+135x^54+70x^55+12x^56+10x^57+3x^58+4x^59+2x^60

The gray image is a code over GF(2) with n=376, k=16 and d=164.
This code was found by Heurico 1.16 in 23.7 seconds.