The generator matrix

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

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+373x^48+1662x^49+3688x^50+6744x^51+9805x^52+14868x^53+18528x^54+19834x^55+18188x^56+15444x^57+10111x^58+6426x^59+3207x^60+1328x^61+528x^62+222x^63+70x^64+24x^65+7x^66+6x^67+2x^68+2x^70+2x^72+2x^73

The gray image is a code over GF(2) with n=440, k=17 and d=192.
This code was found by Heurico 1.16 in 115 seconds.