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

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+325x^52+528x^54+128x^55+1036x^56+256x^57+816x^58+128x^59+628x^60+160x^62+59x^64+23x^68+7x^72+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 34.7 seconds.