The generator matrix

 1  0  1  1  1 X^2+X+2  1  X  1 X^2+2  1  1  1  2  1  1 X^2+X+2  1  1  1 X^2+X  1 X^2  1 X+2  1  1  1  1  1 X^2  1  1  1 X^2+X  1  1  1  1  1  1 X^2+X+2  X  1  1  X  1  1  1  1  X  X  1  1  2 X^2+X+2  1
 0  1 X+1 X^2+X X^2+3  1 X^2+2  1 X^2+X+1  1 X^2+X+2 X^2+1  X  1  3  0  1 X+3 X+2  1  1  2  1 X^2+1  1 X^2  3 X+1 X^2+X+3 X+2  1  1 X^2+X+1 X^2  1  3 X+1 X^2+X+1 X^2+X+1 X^2+3 X^2  1  X X^2+X+3 X^2+X+1  2  1 X^2+X+1 X^2+X  X X^2+2  1 X^2+3  0  1  1  0
 0  0 X^2  0 X^2+2 X^2  0 X^2 X^2+2  2 X^2  0 X^2+2 X^2+2  2  2 X^2+2 X^2+2  2 X^2  0 X^2 X^2  0  2 X^2+2  2  0  0  0 X^2+2 X^2 X^2 X^2+2  2 X^2  2 X^2  2 X^2+2 X^2+2  2  2  0  0 X^2+2 X^2+2 X^2  2  2 X^2 X^2  0 X^2+2 X^2 X^2+2  0
 0  0  0  2  0  0  0  0  2  0  0  2  0  2  2  2  2  2  0  2  2  2  0  0  2  2  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  0  2  0  0
 0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  2  0  2  2  2  0  0  0  2  2  2  0  0  2  0  2  0  2  2  2  0  0  2  2  0  0  0  0  0  2  2  2  0  0  2  0  0  0  0  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+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.