The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+67x^50+272x^51+329x^52+614x^53+407x^54+848x^55+383x^56+562x^57+233x^58+224x^59+86x^60+28x^61+23x^62+10x^65+2x^66+2x^69+2x^70+2x^74+1x^76

The gray image is a code over GF(2) with n=440, k=12 and d=200.
This code was found by Heurico 1.16 in 0.297 seconds.