The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+250x^41+1763x^42+3128x^43+5104x^44+7496x^45+9550x^46+10624x^47+10119x^48+7836x^49+4995x^50+2544x^51+1396x^52+460x^53+192x^54+36x^55+28x^56+6x^57+4x^58+4x^59

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 25.3 seconds.