The generator matrix

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

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+426x^52+984x^53+1596x^54+2088x^55+2205x^56+2316x^57+2122x^58+1828x^59+1277x^60+756x^61+426x^62+176x^63+86x^64+36x^65+46x^66+4x^67+5x^68+4x^69+2x^70

The gray image is a code over GF(2) with n=456, k=14 and d=208.
This code was found by Heurico 1.16 in 2.97 seconds.