The generator matrix

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

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+376x^52+1002x^53+1606x^54+2176x^55+2124x^56+2536x^57+1956x^58+1634x^59+1377x^60+822x^61+381x^62+228x^63+85x^64+38x^65+22x^66+10x^67+5x^68+3x^70+2x^73

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 2.45 seconds.