The generator matrix

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

generates a code of length 57 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+764x^51+1944x^52+3782x^53+5354x^54+7930x^55+8638x^56+9124x^57+8614x^58+7792x^59+5390x^60+3444x^61+1502x^62+764x^63+273x^64+156x^65+18x^66+28x^67+10x^68+6x^69+2x^71

The gray image is a code over GF(2) with n=456, k=16 and d=204.
This code was found by Heurico 1.16 in 32.5 seconds.