The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+378x^45+1698x^46+3710x^47+5496x^48+7314x^49+8893x^50+10378x^51+9497x^52+7654x^53+5082x^54+3034x^55+1459x^56+600x^57+221x^58+78x^59+35x^60+4x^61+2x^62+2x^65

The gray image is a code over GF(2) with n=408, k=16 and d=180.
This code was found by Heurico 1.16 in 27.8 seconds.