The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+394x^45+1684x^46+3388x^47+5957x^48+7108x^49+9604x^50+9556x^51+9750x^52+7148x^53+5462x^54+3102x^55+1598x^56+452x^57+208x^58+64x^59+38x^60+18x^61+2x^62+2x^63

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 26.3 seconds.