The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+716x^51+2033x^52+3824x^53+5461x^54+7560x^55+8541x^56+9402x^57+8650x^58+7858x^59+5408x^60+3262x^61+1593x^62+740x^63+264x^64+126x^65+40x^66+38x^67+9x^68+10x^69

The gray image is a code over GF(2) with n=456, k=16 and d=204.
This code was found by Heurico 1.16 in 45.6 seconds.