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 X^2  1  X  X  1  X
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2 X^2+X  0 X+2 X^2+2 X+2  0 X^2+X+2 X^2+2  2 X^2+X X^2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X X^2+2  X  0 X^2+X+2 X^2  X X^2  0 X^2 X^2+X X^2+X X+2 X+2  2 X^2 X^2+X  X X^2+2 X^2+2 X^2+X X^2+X+2  0  2  X X^2+X+2 X^2+2  X X^2+X X^2+X X+2  0
 0  0  2  0  0  0  2  0  2  0  2  0  2  0  2  0  0  0  2  0  2  2  2  0  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0  2  0  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2  2  0  2  2  0  0  2  2  0  2  2  2  2  0  0  2  0  2  0  2  0  2  0  2  2  0  0  0  0  0  2  2
 0  0  0  0  2  0  2  2  2  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  2  2  2  0  0  0  2  2  0  0  2  0  0  2  0  0  0  0  2  2  2  2  0  0  0  2  0  0  2  0  2
 0  0  0  0  0  2  0  2  2  2  2  2  0  2  0  2  0  2  0  2  0  2  2  0  2  0  2  2  0  0  2  0  0  0  2  0  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0

generates a code of length 57 over Z4[X]/(X^3+2,2X) 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 0.235 seconds.