The generator matrix

 1  0  0  1  1  1  X  1  1 X^2+X  1  0 X^2+X  1  1  1  1 X+2  X X^2+2  1  0 X^2  1  1  X  1  2  1  1  1 X^2  1 X^2+X  1  1  1 X+2  1  X X^2+X  1 X^2  1 X^2 X^2+X+2 X+2  1  1  0 X^2+X+2  1  1  1 X^2+X+2  0  1
 0  1  0  0 X^2+1 X+3  1 X^2+X+3 X^2+X X^2+2 X^2+X+3  1  1 X^2+2 X+2 X^2+X+1 X+3  1  1 X^2+X X^2+X+2  1  1 X^2+X+2  2  X  3  1 X^2+1  1 X^2+3 X^2+2  0  1 X^2+X+1  0  3  1 X+3 X^2+2  X  2  1 X+1  1  1  1 X^2+X  2  1  1 X+3  1 X+1  2  1 X^2+X
 0  0  1  1  1 X^2 X^2+1 X+3  3  1 X^2+X+2 X^2 X^2+X+1 X^2+X X+3 X+2 X^2+1 X+1 X^2+X+2  1 X^2+X X^2+X+1 X^2+X+2  X X+1  1  3 X^2+X+1  0 X+3  2  1  1 X^2+1 X+1 X^2 X+2 X+2  2  1  1  3 X^2+X+3 X+3  0 X^2+2 X^2+X X^2+X+3  2  1 X^2+2 X^2 X^2+X+1 X^2+X  1 X^2+X+3 X^2+1
 0  0  0  X X+2  2 X+2 X^2+X+2  X  X X^2+2 X+2 X^2+2 X^2+X+2 X^2 X+2 X^2 X+2  2  2 X^2+X  X X+2  0 X^2+2  2  0  2  X  X  2 X^2+X X^2+2 X^2+X  2 X^2+X+2 X^2+X+2  X X^2+X+2 X^2+X X+2 X^2+X X^2+X X+2 X^2 X^2+X X^2+2 X+2 X+2  2  0 X^2+2  0 X^2+2  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+194x^51+1016x^52+1968x^53+3030x^54+3486x^55+4495x^56+4680x^57+4503x^58+3648x^59+2763x^60+1466x^61+905x^62+326x^63+140x^64+76x^65+25x^66+26x^67+17x^68+2x^69+1x^70

The gray image is a code over GF(2) with n=456, k=15 and d=204.
This code was found by Heurico 1.16 in 8.2 seconds.