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

generates a code of length 54 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+199x^46+1208x^47+2898x^48+7074x^49+12141x^50+19870x^51+29445x^52+37500x^53+40100x^54+38792x^55+30093x^56+20822x^57+11427x^58+6060x^59+2754x^60+1122x^61+379x^62+130x^63+82x^64+24x^65+10x^66+2x^67+7x^68+2x^69+2x^71

The gray image is a code over GF(2) with n=432, k=18 and d=184.
This code was found by Heurico 1.16 in 468 seconds.