The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+233x^46+1008x^47+1623x^48+1950x^49+2156x^50+2828x^51+2145x^52+1818x^53+1220x^54+810x^55+346x^56+130x^57+43x^58+24x^59+29x^60+6x^61+9x^62+2x^63+3x^66

The gray image is a code over GF(2) with n=408, k=14 and d=184.
This code was found by Heurico 1.16 in 2.12 seconds.