The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+742x^51+2148x^52+3750x^53+5372x^54+7296x^55+8793x^56+9412x^57+8883x^58+7626x^59+5270x^60+3376x^61+1704x^62+684x^63+300x^64+108x^65+35x^66+20x^67+10x^69+6x^70

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 34.5 seconds.