The generator matrix

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

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+510x^51+836x^52+1156x^53+1386x^54+1256x^55+951x^56+668x^57+546x^58+438x^59+195x^60+156x^61+50x^62+36x^63+4x^65+2x^66+1x^68

The gray image is a code over GF(2) with n=440, k=13 and d=204.
This code was found by Heurico 1.16 in 15.8 seconds.