The generator matrix

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

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+216x^47+1241x^48+3102x^49+7420x^50+11688x^51+21263x^52+27424x^53+38965x^54+37820x^55+40616x^56+28112x^57+22023x^58+11276x^59+6374x^60+2748x^61+1159x^62+428x^63+162x^64+50x^65+29x^66+12x^67+7x^68+4x^69+4x^70

The gray image is a code over GF(2) with n=440, k=18 and d=188.
This code was found by Heurico 1.16 in 473 seconds.