The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+145x^52+228x^53+353x^54+532x^55+480x^56+882x^57+413x^58+464x^59+183x^60+106x^61+115x^62+60x^63+82x^64+30x^65+15x^66+4x^68+2x^69+1x^88

The gray image is a code over GF(2) with n=456, k=12 and d=208.
This code was found by Heurico 1.16 in 0.39 seconds.