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  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2  1  X  X  1  X
 0  X  2 3X+2  0 3X+2  2 3X 3X+2  0 3X  2 3X  0 X+2  2 2X 3X+2 2X+2 3X  0 3X+2  2 3X 2X 3X+2  2  X  0 X+2 2X+2  X 2X+2  0 2X+2 3X+2 3X+2 3X 3X 2X 2X+2 3X+2  X  2  2 3X+2 X+2  0 2X  X X+2  2  X 3X+2 3X+2 3X  0
 0  0 2X  0  0  0 2X  0 2X  0 2X  0 2X  0 2X  0  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X  0 2X  0 2X  0 2X
 0  0  0 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0  0  0  0  0 2X 2X
 0  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X  0  0 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0  0 2X  0 2X
 0  0  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X 2X  0  0 2X  0  0  0 2X  0 2X 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  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+103x^52+224x^54+448x^56+512x^57+470x^58+167x^60+100x^62+14x^64+6x^66+2x^68+1x^104

The gray image is a code over GF(2) with n=456, k=11 and d=208.
This code was found by Heurico 1.16 in 0.219 seconds.