The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+309x^52+1000x^53+1822x^54+1924x^55+2339x^56+2384x^57+2098x^58+1624x^59+1259x^60+740x^61+462x^62+240x^63+112x^64+20x^65+34x^66+4x^67+12x^68

The gray image is a code over GF(2) with n=456, k=14 and d=208.
This code was found by Heurico 1.16 in 2.41 seconds.