The generator matrix

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

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+178x^52+208x^53+385x^54+352x^55+630x^56+718x^57+621x^58+344x^59+291x^60+116x^61+115x^62+24x^63+61x^64+30x^65+15x^66+6x^68+1x^92

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 0.391 seconds.