The generator matrix

 1  0  1  1  1 X+2  1  X  1  2  1  1  1 2X  1  1 X+2  1  1  1 3X+2  1 2X+2  1 3X  1  1  1  1  1 2X+2  1  1  1 3X+2  1  1  1  1  1  1 X+2  X  1  1  X  1  1  1  1  X  X  1  1 2X X+2  1
 0  1 X+1 3X+2  3  1  2  1 3X+3  1 X+2 2X+3  X  1 2X+1  0  1 3X+1 3X  1  1 2X  1 2X+3  1 2X+2 2X+1 X+1 X+3 3X  1  1 3X+3 2X+2  1 2X+1 X+1 3X+3 3X+3  3 2X+2  1  X X+3 3X+3 2X  1 3X+3 3X+2  X  2  1  3  0  1  1  0
 0  0 2X+2  0  2 2X+2  0 2X+2  2 2X 2X+2  0  2  2 2X 2X  2  2 2X 2X+2  0 2X+2 2X+2  0 2X  2 2X  0  0  0  2 2X+2 2X+2  2 2X 2X+2 2X 2X+2 2X  2  2 2X 2X  0  0  2  2 2X+2 2X 2X 2X+2 2X+2  0  2 2X+2  2  0
 0  0  0 2X  0  0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0  0
 0  0  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0  0  0 2X 2X 2X  0  0 2X  0  0  0  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+65x^52+294x^53+422x^54+452x^55+501x^56+608x^57+716x^58+410x^59+205x^60+246x^61+105x^62+26x^63+26x^64+4x^65+6x^67+4x^70+2x^71+2x^76+1x^78

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 0.328 seconds.