The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  0  1 X^2+X+2  1  1  1  1  2  1 X+2  1  1  0  1 X+2  1  1  1  1  1  1  1  1 X^2  1  1  1  1  X  1  1 X+2  1  1 X+2 X^2+X X^2  0  1  1  1  1  0  1  1  X X^2+X  1  1
 0  1 X+1 X^2+X+2 X^2+1  1 X^2+3  0  1 X^2+X+2  1 X+1  3 X^2+X+1  2  1 X+2  1 X^2+X+3  0  1 X+2  1  1 X^2+X+3 X^2+3 X+1 X^2+3 X^2+X+3  3 X^2  1 X+1 X+3 X+3  X  1 X^2+3 X^2+X  1  2  3  1  1  1  1 X^2+2 X+3 X^2+3 X^2+1  1 X+1  2  1  1 X^2+1  0
 0  0 X^2  0  0  0  0 X^2 X^2+2 X^2+2 X^2 X^2+2  2 X^2 X^2+2 X^2  2  2 X^2  2  2 X^2 X^2+2  2 X^2+2 X^2  0 X^2  0 X^2  0 X^2+2  2  2  2  0 X^2 X^2+2  0  0 X^2  0  2 X^2  2 X^2  2  2  2  0 X^2 X^2+2 X^2  0  0 X^2  0
 0  0  0 X^2+2  2 X^2+2 X^2 X^2 X^2+2  2  0 X^2+2  0  2  0  2  2  2 X^2+2 X^2+2 X^2+2 X^2 X^2+2 X^2 X^2  0  2 X^2 X^2  2 X^2+2  2  0 X^2 X^2+2 X^2  2  0  0  0  2  2 X^2 X^2+2 X^2 X^2  0  2 X^2  0 X^2+2  0  0 X^2+2  2  2  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+90x^52+270x^53+302x^54+608x^55+515x^56+572x^57+506x^58+588x^59+279x^60+252x^61+83x^62+4x^63+8x^64+8x^65+2x^66+2x^68+2x^69+2x^70+1x^78+1x^84

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 0.282 seconds.